Project 350B: Analysing Ames Housing Dataset
Anish Mohan
March 15, 2017
Analysing Ames Housing Dataset.
Credit: This data was was obtained from https://ww2.amstat.org/publications/jse/v19n3/decock.pdf and is also available as part of Kaggle Competition: https://www.kaggle.com/c/house-prices-advanced-regression-techniques
Introduction
The Ames Housing data has many details regarding houses sold and bought in Ames, Iowas between 2006 - 2010. It has details of 81 metrics related to theses houses. The features includes common aspects of house like Area of the Lot, Area of the house, Number of bathrooms etc. It also includes some uncommon aspects like the Masonary Veneer type, 3 Season porch etc. The data contains information about 1451 houses.
Overview and Summary of Results
In this report we perform some exploratory data analysis on the housing data from Ames,Iowa. One of the key aspects
Exploratory Data Analysis
In the given data, about half of the features are Quantitiative variables and the remaining ones are Categorical variables. There are many houses that do not have all the feature information available. Also there are many features or variables which are only available for small number of houses.
In this analysis, we will consider the House Sale Price as the dependent variable and rest of the variables being independent variables.
#Loading the libraries and the data
library(ggplot2)
library(reshape2)
library(MASS)
house = read.csv("train.csv", header = TRUE, stringsAsFactors = FALSE)
house[complete.cases(house),]## [1] Id MSSubClass MSZoning LotFrontage LotArea
## [6] Street Alley LotShape LandContour Utilities
## [11] LotConfig LandSlope Neighborhood Condition1 Condition2
## [16] BldgType HouseStyle OverallQual OverallCond YearBuilt
## [21] YearRemodAdd RoofStyle RoofMatl Exterior1st Exterior2nd
## [26] MasVnrType MasVnrArea ExterQual ExterCond Foundation
## [31] BsmtQual BsmtCond BsmtExposure BsmtFinType1 BsmtFinSF1
## [36] BsmtFinType2 BsmtFinSF2 BsmtUnfSF TotalBsmtSF Heating
## [41] HeatingQC CentralAir Electrical X1stFlrSF X2ndFlrSF
## [46] LowQualFinSF GrLivArea BsmtFullBath BsmtHalfBath FullBath
## [51] HalfBath BedroomAbvGr KitchenAbvGr KitchenQual TotRmsAbvGrd
## [56] Functional Fireplaces FireplaceQu GarageType GarageYrBlt
## [61] GarageFinish GarageCars GarageArea GarageQual GarageCond
## [66] PavedDrive WoodDeckSF OpenPorchSF EnclosedPorch X3SsnPorch
## [71] ScreenPorch PoolArea PoolQC Fence MiscFeature
## [76] MiscVal MoSold YrSold SaleType SaleCondition
## [81] SalePrice
## <0 rows> (or 0-length row.names)# names(house)
dim(house)## [1] 1460 81# str(house)Since some variables are only available for small number of houses, for the purpose of the analysis here, I have removed them as they would have significant impact on most of the houses. I do understand the implication here that such variable might be a good predictor for the dependent variable:- House Sale Price
todrop = c("Fence", "MiscFeature","PoolQC","GarageType","GarageQual","GarageCond", "GarageFinish","GarageYrBlt",
"FireplaceQu", "BsmtFinType1", "BsmtFinType2", "BsmtExposure","BsmtQual","BsmtCond","Alley","LotFrontage","Condition2")
house[,todrop] = NULL
house = na.omit(house)
house.int = house[,c("MSSubClass","LotArea","OverallQual","OverallCond",
"MasVnrArea","BsmtFinSF1","BsmtFinSF2","BsmtUnfSF","TotalBsmtSF",
"X1stFlrSF","X2ndFlrSF","LowQualFinSF","GrLivArea","BsmtFullBath",
"BsmtHalfBath","FullBath","HalfBath","BedroomAbvGr","KitchenAbvGr",
"TotRmsAbvGrd","Fireplaces","GarageCars","GarageArea",
"WoodDeckSF","OpenPorchSF","EnclosedPorch","X3SsnPorch","PoolArea",
"MiscVal","MoSold","YrSold","SalePrice")]Summary of the housing data shows some interesting results in the distribution of the features. For e.g + Lot Are of the house has a huge variation and can vary from 1300 Sq Ft to 200,000Sq Ft. The lot area for the some of the houses are smaller than the Basement area of some of the other houses.
There is a subjective measurement of Overall Quality of the house that rates from 1 to Max Quality of 10 with the median about 6. Another subjective measurement is the Overall Condition of the house that varies from 1 to 9 with the median about 5.
Most houses have atleast 1 room. However, some houses are sold even without any bathrooms or half bathrooms.
The Sale price has a huge variance going from about$ 35K to $755K
summary(house.int)## MSSubClass LotArea OverallQual OverallCond
## Min. : 20.00 Min. : 1300 Min. : 1.000 Min. :1.00
## 1st Qu.: 20.00 1st Qu.: 7538 1st Qu.: 5.000 1st Qu.:5.00
## Median : 50.00 Median : 9477 Median : 6.000 Median :5.00
## Mean : 56.93 Mean : 10508 Mean : 6.094 Mean :5.58
## 3rd Qu.: 70.00 3rd Qu.: 11600 3rd Qu.: 7.000 3rd Qu.:6.00
## Max. :190.00 Max. :215245 Max. :10.000 Max. :9.00
## MasVnrArea BsmtFinSF1 BsmtFinSF2 BsmtUnfSF
## Min. : 0.0 Min. : 0.0 Min. : 0.00 Min. : 0.0
## 1st Qu.: 0.0 1st Qu.: 0.0 1st Qu.: 0.00 1st Qu.: 222.0
## Median : 0.0 Median : 381.0 Median : 0.00 Median : 479.0
## Mean : 103.8 Mean : 442.3 Mean : 46.84 Mean : 567.2
## 3rd Qu.: 166.0 3rd Qu.: 707.0 3rd Qu.: 0.00 3rd Qu.: 808.0
## Max. :1600.0 Max. :5644.0 Max. :1474.00 Max. :2336.0
## TotalBsmtSF X1stFlrSF X2ndFlrSF LowQualFinSF
## Min. : 0 Min. : 334 Min. : 0.0 Min. : 0.000
## 1st Qu.: 795 1st Qu.: 882 1st Qu.: 0.0 1st Qu.: 0.000
## Median : 991 Median :1086 Median : 0.0 Median : 0.000
## Mean :1056 Mean :1162 Mean : 346.7 Mean : 5.881
## 3rd Qu.:1298 3rd Qu.:1391 3rd Qu.: 728.0 3rd Qu.: 0.000
## Max. :6110 Max. :4692 Max. :2065.0 Max. :572.000
## GrLivArea BsmtFullBath BsmtHalfBath FullBath
## Min. : 334 Min. :0.0000 Min. :0.00000 Min. :0.000
## 1st Qu.:1128 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:1.000
## Median :1464 Median :0.0000 Median :0.00000 Median :2.000
## Mean :1514 Mean :0.4238 Mean :0.05789 Mean :1.562
## 3rd Qu.:1776 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:2.000
## Max. :5642 Max. :3.0000 Max. :2.00000 Max. :3.000
## HalfBath BedroomAbvGr KitchenAbvGr TotRmsAbvGrd
## Min. :0.0000 Min. :0.000 Min. :0.000 Min. : 2.000
## 1st Qu.:0.0000 1st Qu.:2.000 1st Qu.:1.000 1st Qu.: 5.000
## Median :0.0000 Median :3.000 Median :1.000 Median : 6.000
## Mean :0.3811 Mean :2.867 Mean :1.046 Mean : 6.517
## 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:1.000 3rd Qu.: 7.000
## Max. :2.0000 Max. :8.000 Max. :3.000 Max. :14.000
## Fireplaces GarageCars GarageArea WoodDeckSF
## Min. :0.0000 Min. :0.000 Min. : 0.0 Min. : 0.00
## 1st Qu.:0.0000 1st Qu.:1.000 1st Qu.: 327.5 1st Qu.: 0.00
## Median :1.0000 Median :2.000 Median : 478.0 Median : 0.00
## Mean :0.6127 Mean :1.765 Mean : 472.5 Mean : 94.41
## 3rd Qu.:1.0000 3rd Qu.:2.000 3rd Qu.: 576.0 3rd Qu.:168.00
## Max. :3.0000 Max. :4.000 Max. :1418.0 Max. :857.00
## OpenPorchSF EnclosedPorch X3SsnPorch PoolArea
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0.000
## Median : 24.00 Median : 0.00 Median : 0.000 Median : 0.000
## Mean : 46.42 Mean : 21.95 Mean : 3.431 Mean : 2.776
## 3rd Qu.: 68.00 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0.000
## Max. :547.00 Max. :552.00 Max. :508.000 Max. :738.000
## MiscVal MoSold YrSold SalePrice
## Min. : 0.00 Min. : 1.000 Min. :2006 Min. : 34900
## 1st Qu.: 0.00 1st Qu.: 5.000 1st Qu.:2007 1st Qu.:129900
## Median : 0.00 Median : 6.000 Median :2008 Median :162500
## Mean : 43.76 Mean : 6.319 Mean :2008 Mean :180624
## 3rd Qu.: 0.00 3rd Qu.: 8.000 3rd Qu.:2009 3rd Qu.:214000
## Max. :15500.00 Max. :12.000 Max. :2010 Max. :755000Analysing Histogram Distributions of data
Histogram of Sale distribution shows a peak around $150K, with a long tail going upto $750K
ggplot(house, aes(SalePrice)) + geom_histogram(binwidth = 10000) + xlab("SalePrice") + ylab("Counts") + ggtitle(" Histogram of Sale Prices")
Histogram of the Quality Ratings shows that most Houses have a quality rating of 5 or 6.
ggplot(house, aes(OverallQual)) + geom_histogram() + xlab("Quality Ratings") + ylab("Counts") + ggtitle(" Histogram of Quality Rating of Houses")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Histogram for the total housing area shows a very broad peak of about 1000-2000 Square feet.
ggplot(house, aes(X1stFlrSF+X2ndFlrSF)) + geom_histogram(binwidth = 100) + xlab("Total Housing Area Square Feet") + ylab("Counts") + ggtitle("Histogram of House Area")
Histogram of Garage distribution shows that most of the sold houses have garage capacity of 2 Cars
ggplot(house, aes(GarageCars)) + geom_histogram() + xlab("Garage Capacity") + ylab("Counts") + ggtitle("Histogram of Garage Capacity")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Similar to Garage Capacity, the distribution of # of full baths show that most houses have 2 baths.
ggplot(house, aes(FullBath)) + geom_histogram() + xlab("# of Full Bath") + ylab("Counts") + ggtitle("Histogram of Full Baths")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Looking at distriubtion of Buidling types, Single Family houses are the most common houses that sold.
ggplot(house, aes(BldgType)) + geom_bar() + xlab("# of Full Bath") + ylab("Counts") + ggtitle("Bar chart of Building Types")
This bar chart shows that 1 and 2 story houses are the most common. In such houses both the 1st and 2nd level of the houses are finished.
ggplot(house, aes(HouseStyle)) + geom_bar() + xlab("House Style") + ylab("Counts") + ggtitle("Chart of Style of the Houses")
The distribution of the ZOning of the sold houses show that most houses sold are in the Residential Low Density Zones.
ggplot(house, aes(MSZoning)) + geom_bar() + xlab("Zoning Type") + ylab("Counts") + ggtitle("Bar chart of Location Zone of the houses")
Analysing Covariance/Correation between variables.
Analysis of co-variance and correlations show that houses built in latter years have higher quality rating. The overall quality rating also seems to be higher when the houses are larger having bigger basement and living areas. Such houses are also sold at higher Sale price.
Sale Price seeems to be impacted by overall the size of the house. Basically, if the house has larger area, it also means that it has larger 1st floor area, Living area and Basement area etc.
options(repr.plot.width=16, repr.plot.height=16)
require(car)## Loading required package: carscatterplotMatrix(~LotArea + YearBuilt+ OverallQual + TotalBsmtSF + X1stFlrSF + GrLivArea +SalePrice, data = house)
Second set of factors that seem to impact Sale price is the number of Bedrooms. Bathrooms and higher capacity garages.
## Warning in smoother(x, y, col = col[2], log.x = FALSE, log.y = FALSE,
## spread = spread, : could not fit negative part of the spread
## Warning in smoother(x, y, col = col[2], log.x = FALSE, log.y = FALSE,
## spread = spread, : could not fit negative part of the spread
Correlation Plots
This correlatin plot shows that there is positive correlation of Overall Quality, Total Basement Area, 1St Floor Area, Greater Living area, Number of full baths, Total Rooms, Number ofFireplaces, Garage Area etc.
There also seems to be correlation on the charactersitcs of the home i.e a home with larger 1st floor area has higher total basement area, living area , garage area etc.
library(ellipse)##
## Attaching package: 'ellipse'## The following object is masked from 'package:car':
##
## ellipseR = cor(house[, c("MSSubClass","LotArea","OverallQual","OverallCond",
"TotalBsmtSF","X1stFlrSF","GrLivArea","FullBath","HalfBath","BedroomAbvGr","KitchenAbvGr","TotRmsAbvGrd","Fireplaces","GarageCars","GarageArea",
"WoodDeckSF","OpenPorchSF","EnclosedPorch","X3SsnPorch","PoolArea",
"SalePrice")], method = 'pearson')
#print(R)
options(repr.plot.width=50, repr.plot.height=50)
Lab.palette <- colorRampPalette(c("red", "orange", "blue"),
space = "Lab")
plotcorr(R, col = Lab.palette(25))
This correlatin plot shows that there is positive correlation of Overall Quality, Total Basement Area, 1St Floor Area, Greater Living area, Number of full baths, Total Rooms, Number ofFireplaces, Garage Area etc.
There also seems to be correlation on the charactersitcs of the home i.e a home with larger 1st floor area has higher total basement area, living area , garage area etc.
Also, this shows that a house with higher overall quality generally has larger living size and generally fetches higher price.
library(corrplot)
corrplot(R, method="circle", type='lower')
Comparing impact of specific variables to Sales Price
This comparison shows that Houses with Central air system sell at higher price than houses without central air.
ggplot(house, aes(x = factor(CentralAir), y = SalePrice)) + geom_boxplot() + xlab("Central Air") + ylab("Sale Price") + ggtitle("Distribution of Sale Price based on Central Air system")
This chart shows that Sales price is uniform among building types, but there is a lot of variation in Single Family homes compared to other building types
ggplot(house, aes(x = factor(BldgType), y = SalePrice)) + geom_violin(trim = T, draw_quantiles = c(0.25,0.5,0.75)) + xlab("Building Type") + ylab("Sale Price") + ggtitle("Distribution of Sale Price based on Building Type")
This chart shows that houses with wood shingle roof generally prefer high prices compared to Composite shingle roof or Tar Gravel roof
ggplot(house, aes(x = factor(RoofMatl), y = SalePrice)) + geom_violin(trim = T, draw_quantiles = c(0.25,0.5,0.75)) + xlab("Roof Material") + ylab("Sale Price") + ggtitle("Distribution of Sale Price based on Roof Material")
Next charts show that houses with more full baths and garages fetch higher prices
ggplot(house, aes(x = factor(GarageCars), y = SalePrice)) + geom_violin(trim = T, draw_quantiles = c(0.25,0.5,0.75)) + xlab("Garage Cars") + ylab("Sale Price") + ggtitle("Distribution of Sale Price based on Garage Cars")
ggplot(house, aes(x = factor(FullBath), y = SalePrice)) + geom_violin(trim = T, draw_quantiles = c(0.25,0.5,0.75)) + xlab("Full Bath") + ylab("Sale Price") + ggtitle("Distribution of Sale Price based on Full Bath")
This chart shows that houses with higher quality rating have are sold at higher prices
ggplot(house, aes(x = factor(OverallQual), y = SalePrice)) + geom_violin(trim = T, draw_quantiles = c(0.25,0.5,0.75)) + xlab("Quality of house") + ylab("Sale Price") + ggtitle("Distribution of Sale Price based on Quality of house")
Point Distribution of paried variables.
This distribution clearly shows that houses on RM Zone (Residential Medium Denisity) have lower lot area and generally have lower sales price
ggplot(house, aes(y = SalePrice, x = log(LotArea))) + geom_point(aes(color= factor(MSZoning))) + xlab("Log(Lot Area)") + ylab("Sale Price") + ggtitle("Relationship between Lot Area, Sale Price and Zoning")
This distribution chart shows that generally Townhomes are on lower lot area and feth lower prices. However End unit townhouses fetch comparable prices to single family homes
ggplot(house, aes(y = SalePrice, x = log(LotArea))) + geom_point(aes(color= factor(BldgType))) + xlab("Lot Area") + ylab("Sale Price") + ggtitle("Relationship between Lot Area, Sale Price and Building Type ")
This chart clearly shows that houses that are built in later years are geneally more expensive even if they might have the same area
ggplot(house, aes(y = SalePrice, x = (X1stFlrSF+X2ndFlrSF))) + geom_point(aes(color= factor(YearBuilt))) + xlab("House Area") + ylab("Sale Price") + ggtitle("Relationship between House Area, Sale Price and Year built")
This chart shows that foundation impacts the price of the house and the most expensive houses have pourded concrete foundation.
ggplot(house, aes(y = SalePrice, x = (X1stFlrSF + X2ndFlrSF))) + geom_point(aes(color= factor(Foundation))) + xlab("House Area") + ylab("Sale Price") + ggtitle("Relationship between House Area, Sale Price and Foundation")
Regression
Results of the regression analysis shows that the following variables are good for predicting the Sale Price of the house. These variable have a p-value of <0.01
1. Overall Quality of house
2. Overall Condition of the house
3. Year that house was built
4. Heating
5. Zoning
6. Condition of House
7. Roof Material
8. Basement paramters
9. Kitchen parametersThe final results has following parameters:
1. RMSE of about 0.1099
2. $R^2$ = 0.93
3. Adj $R^2$ = 0.92#Linear Regression of the model.
house$logSalePrice = log(house$SalePrice)
lm.house = lm(logSalePrice ~.-SalePrice,data = house)summary(lm.house)##
## Call:
## lm(formula = logSalePrice ~ . - SalePrice, data = house)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.29433 -0.04631 0.00094 0.05470 0.46127
##
## Coefficients: (3 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.618e+00 4.909e+00 1.144 0.252660
## Id -8.153e-06 7.365e-06 -1.107 0.268486
## MSSubClass -5.020e-04 3.920e-04 -1.281 0.200553
## MSZoningFV 4.493e-01 5.665e-02 7.930 4.77e-15 ***
## MSZoningRH 4.226e-01 5.622e-02 7.517 1.06e-13 ***
## MSZoningRL 4.212e-01 4.784e-02 8.805 < 2e-16 ***
## MSZoningRM 3.844e-01 4.482e-02 8.576 < 2e-16 ***
## LotArea 2.132e-06 4.911e-07 4.341 1.53e-05 ***
## StreetPave 1.196e-01 5.595e-02 2.138 0.032686 *
## LotShapeIR2 3.733e-02 1.978e-02 1.887 0.059370 .
## LotShapeIR3 4.827e-02 4.154e-02 1.162 0.245443
## LotShapeReg 4.003e-03 7.620e-03 0.525 0.599431
## LandContourHLS 5.993e-02 2.411e-02 2.485 0.013068 *
## LandContourLow 2.363e-02 2.974e-02 0.795 0.426984
## LandContourLvl 4.933e-02 1.745e-02 2.827 0.004778 **
## UtilitiesNoSeWa -2.471e-01 1.224e-01 -2.020 0.043605 *
## LotConfigCulDSac 3.158e-02 1.523e-02 2.073 0.038384 *
## LotConfigFR2 -3.370e-02 1.904e-02 -1.770 0.076965 .
## LotConfigFR3 -9.190e-02 5.900e-02 -1.558 0.119569
## LotConfigInside -1.495e-02 8.269e-03 -1.807 0.070945 .
## LandSlopeMod 4.321e-02 1.843e-02 2.345 0.019192 *
## LandSlopeSev -9.626e-02 4.971e-02 -1.936 0.053040 .
## NeighborhoodBlueste -4.164e-02 8.894e-02 -0.468 0.639742
## NeighborhoodBrDale -6.615e-02 5.174e-02 -1.279 0.201296
## NeighborhoodBrkSide 3.982e-03 4.407e-02 0.090 0.928014
## NeighborhoodClearCr 2.563e-02 4.353e-02 0.589 0.556184
## NeighborhoodCollgCr -1.905e-02 3.410e-02 -0.559 0.576468
## NeighborhoodCrawfor 1.063e-01 4.024e-02 2.641 0.008366 **
## NeighborhoodEdwards -9.924e-02 3.770e-02 -2.632 0.008588 **
## NeighborhoodGilbert -2.124e-02 3.655e-02 -0.581 0.561246
## NeighborhoodIDOTRR -3.974e-02 5.028e-02 -0.790 0.429471
## NeighborhoodMeadowV -1.444e-01 5.300e-02 -2.724 0.006535 **
## NeighborhoodMitchel -6.037e-02 3.850e-02 -1.568 0.117071
## NeighborhoodNAmes -4.316e-02 3.681e-02 -1.173 0.241189
## NeighborhoodNoRidge 4.489e-02 3.963e-02 1.133 0.257581
## NeighborhoodNPkVill 6.565e-03 6.610e-02 0.099 0.920906
## NeighborhoodNridgHt 8.452e-02 3.490e-02 2.421 0.015603 *
## NeighborhoodNWAmes -3.976e-02 3.767e-02 -1.055 0.291473
## NeighborhoodOldTown -6.696e-02 4.501e-02 -1.488 0.137069
## NeighborhoodSawyer -3.567e-02 3.827e-02 -0.932 0.351473
## NeighborhoodSawyerW -1.544e-02 3.657e-02 -0.422 0.672983
## NeighborhoodSomerst 2.387e-02 4.251e-02 0.561 0.574632
## NeighborhoodStoneBr 1.435e-01 3.918e-02 3.662 0.000260 ***
## NeighborhoodSWISU -9.304e-03 4.553e-02 -0.204 0.838121
## NeighborhoodTimber 4.970e-03 3.880e-02 0.128 0.898087
## NeighborhoodVeenker 5.318e-02 4.964e-02 1.071 0.284199
## Condition1Feedr 1.775e-02 2.265e-02 0.784 0.433333
## Condition1Norm 7.598e-02 1.866e-02 4.072 4.95e-05 ***
## Condition1PosA 3.764e-02 4.683e-02 0.804 0.421655
## Condition1PosN -2.453e-02 3.317e-02 -0.740 0.459723
## Condition1RRAe -4.707e-02 4.273e-02 -1.102 0.270851
## Condition1RRAn 4.363e-02 3.056e-02 1.428 0.153567
## Condition1RRNe -3.138e-04 8.398e-02 -0.004 0.997019
## Condition1RRNn 8.992e-02 5.911e-02 1.521 0.128448
## BldgType2fmCon 6.035e-02 5.874e-02 1.027 0.304450
## BldgTypeDuplex -8.136e-03 3.451e-02 -0.236 0.813673
## BldgTypeTwnhs -5.486e-02 4.693e-02 -1.169 0.242696
## BldgTypeTwnhsE -3.175e-03 4.235e-02 -0.075 0.940252
## HouseStyle1.5Unf -1.561e-02 3.580e-02 -0.436 0.662904
## HouseStyle1Story -3.966e-02 1.995e-02 -1.988 0.047054 *
## HouseStyle2.5Fin -4.279e-02 5.611e-02 -0.763 0.445889
## HouseStyle2.5Unf 8.498e-02 4.150e-02 2.048 0.040784 *
## HouseStyle2Story -9.557e-03 1.618e-02 -0.591 0.554921
## HouseStyleSFoyer 4.632e-03 2.843e-02 0.163 0.870622
## HouseStyleSLvl 8.071e-03 2.543e-02 0.317 0.750971
## OverallQual 4.568e-02 4.694e-03 9.732 < 2e-16 ***
## OverallCond 3.722e-02 4.009e-03 9.285 < 2e-16 ***
## YearBuilt 1.714e-03 3.364e-04 5.093 4.06e-07 ***
## YearRemodAdd 6.968e-04 2.552e-04 2.730 0.006420 **
## RoofStyleGable -3.462e-02 8.584e-02 -0.403 0.686745
## RoofStyleGambrel -3.458e-02 9.380e-02 -0.369 0.712485
## RoofStyleHip -2.930e-02 8.610e-02 -0.340 0.733690
## RoofStyleMansard -1.073e-03 9.996e-02 -0.011 0.991439
## RoofStyleShed 1.256e-01 1.271e-01 0.988 0.323488
## RoofMatlCompShg 2.453e+00 1.503e-01 16.318 < 2e-16 ***
## RoofMatlMembran 2.774e+00 2.175e-01 12.758 < 2e-16 ***
## RoofMatlMetal 2.572e+00 2.150e-01 11.964 < 2e-16 ***
## RoofMatlRoll 2.507e+00 1.904e-01 13.167 < 2e-16 ***
## RoofMatlTar&Grv 2.473e+00 1.731e-01 14.288 < 2e-16 ***
## RoofMatlWdShake 2.465e+00 1.665e-01 14.808 < 2e-16 ***
## RoofMatlWdShngl 2.601e+00 1.565e-01 16.623 < 2e-16 ***
## Exterior1stAsphShn 5.147e-03 1.562e-01 0.033 0.973719
## Exterior1stBrkComm -1.810e-01 1.311e-01 -1.381 0.167631
## Exterior1stBrkFace 1.039e-01 5.825e-02 1.783 0.074762 .
## Exterior1stCBlock -4.261e-02 1.261e-01 -0.338 0.735510
## Exterior1stCemntBd -7.423e-02 8.881e-02 -0.836 0.403408
## Exterior1stHdBoard 8.678e-03 5.874e-02 0.148 0.882569
## Exterior1stImStucc -3.357e-02 1.309e-01 -0.256 0.797708
## Exterior1stMetalSd 6.697e-02 6.719e-02 0.997 0.319087
## Exterior1stPlywood 3.834e-03 5.822e-02 0.066 0.947500
## Exterior1stStone -3.390e-03 1.118e-01 -0.030 0.975818
## Exterior1stStucco 4.886e-02 6.417e-02 0.761 0.446508
## Exterior1stVinylSd 1.522e-02 6.108e-02 0.249 0.803319
## Exterior1stWd Sdng -7.768e-03 5.613e-02 -0.138 0.889946
## Exterior1stWdShing 1.679e-02 6.081e-02 0.276 0.782576
## Exterior2ndAsphShn 3.763e-02 1.039e-01 0.362 0.717225
## Exterior2ndBrk Cmn 2.844e-02 9.455e-02 0.301 0.763659
## Exterior2ndBrkFace -3.331e-02 6.035e-02 -0.552 0.581026
## Exterior2ndCBlock NA NA NA NA
## Exterior2ndCmentBd 1.052e-01 8.768e-02 1.199 0.230607
## Exterior2ndHdBoard 1.362e-02 5.658e-02 0.241 0.809747
## Exterior2ndImStucc 4.730e-02 6.581e-02 0.719 0.472415
## Exterior2ndMetalSd -1.342e-02 6.573e-02 -0.204 0.838254
## Exterior2ndOther -6.943e-02 1.293e-01 -0.537 0.591373
## Exterior2ndPlywood 2.058e-02 5.490e-02 0.375 0.707871
## Exterior2ndStone 1.688e-02 8.470e-02 0.199 0.842061
## Exterior2ndStucco -4.801e-03 6.185e-02 -0.078 0.938141
## Exterior2ndVinylSd 3.336e-02 5.904e-02 0.565 0.572218
## Exterior2ndWd Sdng 4.136e-02 5.430e-02 0.762 0.446367
## Exterior2ndWd Shng -1.467e-03 5.674e-02 -0.026 0.979373
## MasVnrTypeBrkFace 4.140e-02 3.211e-02 1.289 0.197515
## MasVnrTypeNone 3.080e-02 3.236e-02 0.952 0.341405
## MasVnrTypeStone 5.333e-02 3.402e-02 1.568 0.117208
## MasVnrArea -5.618e-06 2.727e-05 -0.206 0.836825
## ExterQualFa 4.538e-02 4.967e-02 0.914 0.361056
## ExterQualGd 1.138e-02 2.208e-02 0.516 0.606224
## ExterQualTA 1.255e-02 2.449e-02 0.512 0.608528
## ExterCondFa -1.576e-01 7.445e-02 -2.117 0.034461 *
## ExterCondGd -1.274e-01 6.949e-02 -1.833 0.067030 .
## ExterCondPo -1.951e-01 1.433e-01 -1.361 0.173605
## ExterCondTA -1.091e-01 6.940e-02 -1.572 0.116192
## FoundationCBlock 2.133e-02 1.463e-02 1.458 0.145204
## FoundationPConc 4.442e-02 1.604e-02 2.769 0.005699 **
## FoundationSlab -1.939e-02 3.597e-02 -0.539 0.589937
## FoundationStone 1.423e-01 5.111e-02 2.785 0.005437 **
## FoundationWood -1.071e-01 6.923e-02 -1.546 0.122272
## BsmtFinSF1 1.310e-04 2.033e-05 6.445 1.64e-10 ***
## BsmtFinSF2 8.984e-05 2.650e-05 3.390 0.000719 ***
## BsmtUnfSF 6.664e-05 1.867e-05 3.570 0.000371 ***
## TotalBsmtSF NA NA NA NA
## HeatingGasA 1.391e-01 1.164e-01 1.196 0.232062
## HeatingGasW 2.067e-01 1.201e-01 1.722 0.085393 .
## HeatingGrav -8.629e-03 1.265e-01 -0.068 0.945608
## HeatingOthW 1.088e-01 1.449e-01 0.751 0.452833
## HeatingWall 2.282e-01 1.349e-01 1.691 0.091065 .
## HeatingQCFa -3.302e-02 2.167e-02 -1.524 0.127751
## HeatingQCGd -2.082e-02 9.833e-03 -2.118 0.034386 *
## HeatingQCPo -7.924e-02 1.269e-01 -0.625 0.532365
## HeatingQCTA -3.248e-02 9.697e-03 -3.349 0.000835 ***
## CentralAirY 5.723e-02 1.814e-02 3.156 0.001639 **
## ElectricalFuseF -1.113e-02 2.752e-02 -0.404 0.685940
## ElectricalFuseP -5.187e-02 7.980e-02 -0.650 0.515848
## ElectricalMix 1.303e-01 1.324e-01 0.985 0.324985
## ElectricalSBrkr -1.586e-02 1.382e-02 -1.148 0.251341
## X1stFlrSF 2.408e-04 2.435e-05 9.886 < 2e-16 ***
## X2ndFlrSF 1.867e-04 2.428e-05 7.688 2.99e-14 ***
## LowQualFinSF 1.655e-04 8.460e-05 1.956 0.050677 .
## GrLivArea NA NA NA NA
## BsmtFullBath 3.481e-02 9.004e-03 3.866 0.000116 ***
## BsmtHalfBath 5.851e-03 1.426e-02 0.410 0.681715
## FullBath 2.089e-02 1.029e-02 2.031 0.042476 *
## HalfBath 2.130e-02 9.804e-03 2.173 0.029967 *
## BedroomAbvGr 5.884e-03 6.358e-03 0.925 0.354904
## KitchenAbvGr -4.772e-02 2.644e-02 -1.805 0.071295 .
## KitchenQualFa -6.222e-02 2.918e-02 -2.132 0.033181 *
## KitchenQualGd -6.468e-02 1.595e-02 -4.055 5.32e-05 ***
## KitchenQualTA -7.040e-02 1.829e-02 -3.850 0.000124 ***
## TotRmsAbvGrd 7.948e-03 4.460e-03 1.782 0.075010 .
## FunctionalMaj2 -2.621e-01 6.857e-02 -3.822 0.000139 ***
## FunctionalMin1 1.255e-02 4.048e-02 0.310 0.756648
## FunctionalMin2 1.791e-03 4.028e-02 0.044 0.964553
## FunctionalMod -7.542e-02 4.907e-02 -1.537 0.124583
## FunctionalSev -2.807e-01 1.299e-01 -2.161 0.030912 *
## FunctionalTyp 5.127e-02 3.507e-02 1.462 0.144025
## Fireplaces 2.724e-02 6.289e-03 4.332 1.60e-05 ***
## GarageCars 3.017e-02 1.015e-02 2.974 0.002997 **
## GarageArea 9.569e-05 3.474e-05 2.755 0.005957 **
## PavedDriveP 2.145e-02 2.546e-02 0.842 0.399737
## PavedDriveY 2.634e-02 1.567e-02 1.681 0.093105 .
## WoodDeckSF 1.060e-04 2.728e-05 3.888 0.000106 ***
## OpenPorchSF 7.126e-05 5.440e-05 1.310 0.190463
## EnclosedPorch 1.328e-04 5.862e-05 2.265 0.023700 *
## X3SsnPorch 2.078e-04 1.059e-04 1.962 0.050028 .
## ScreenPorch 2.846e-04 5.763e-05 4.938 8.95e-07 ***
## PoolArea 1.471e-04 8.437e-05 1.743 0.081603 .
## MiscVal -4.415e-06 6.439e-06 -0.686 0.493058
## MoSold -1.237e-03 1.166e-03 -1.060 0.289229
## YrSold -1.358e-03 2.416e-03 -0.562 0.574049
## SaleTypeCon 8.633e-02 8.415e-02 1.026 0.305152
## SaleTypeConLD 1.513e-01 4.559e-02 3.319 0.000929 ***
## SaleTypeConLI -3.266e-02 5.459e-02 -0.598 0.549800
## SaleTypeConLw 9.420e-03 5.686e-02 0.166 0.868445
## SaleTypeCWD 8.052e-02 6.128e-02 1.314 0.189033
## SaleTypeNew 1.323e-01 7.333e-02 1.804 0.071468 .
## SaleTypeOth 9.021e-02 6.886e-02 1.310 0.190412
## SaleTypeWD -2.113e-02 1.988e-02 -1.063 0.287894
## SaleConditionAdjLand 1.171e-01 6.875e-02 1.703 0.088855 .
## SaleConditionAlloca 1.042e-01 4.188e-02 2.488 0.012962 *
## SaleConditionFamily 8.949e-03 2.895e-02 0.309 0.757271
## SaleConditionNormal 7.236e-02 1.369e-02 5.286 1.47e-07 ***
## SaleConditionPartial -3.875e-02 7.071e-02 -0.548 0.583790
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1099 on 1263 degrees of freedom
## Multiple R-squared: 0.9341, Adjusted R-squared: 0.9244
## F-statistic: 95.75 on 187 and 1263 DF, p-value: < 2.2e-16Plotting of various residual values show that * Residuals are mean distributed at 0. * There are some values that have high leverage and some that are outliers.
plot(lm.house)
Stepwise regression
Stepwise regression shows that there is lot of correlation between the independent variable. The final model was a combination of following parameters
1. Land/Lot Parameters (Contour, Utilities, Slope, Zoning etc. )
2. Areas of various parts of the house( Lot Area, Garage Area etc )
3. Roof Material
4. Characterstics, Quality and Condition of the house.
5. Number of rooms, garages, full baths, half baths.
6. Heating and Central Air.
7. Basement size parametersSome of the parameters that were removed from the model were:
1. Class of the land
2. Shape of the lot
3. House Style
4. Roof Styles
5. Anything to do with Masonary.
6. Basement Conditionslm.house.aic = stepAIC(lm.house, direction = "both")## Start: AIC=-6234.11
## logSalePrice ~ (Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl +
## Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + ExterQual +
## ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF +
## TotalBsmtSF + Heating + HeatingQC + CentralAir + Electrical +
## X1stFlrSF + X2ndFlrSF + LowQualFinSF + GrLivArea + BsmtFullBath +
## BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr +
## KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageCars +
## GarageArea + PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch +
## X3SsnPorch + ScreenPorch + PoolArea + MiscVal + MoSold +
## YrSold + SaleType + SaleCondition + SalePrice) - SalePrice
##
##
## Step: AIC=-6234.11
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl +
## Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + ExterQual +
## ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF +
## TotalBsmtSF + Heating + HeatingQC + CentralAir + Electrical +
## X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath +
## FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual +
## TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea +
## PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch +
## ScreenPorch + PoolArea + MiscVal + MoSold + YrSold + SaleType +
## SaleCondition
##
##
## Step: AIC=-6234.11
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl +
## Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + ExterQual +
## ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF +
## Heating + HeatingQC + CentralAir + Electrical + X1stFlrSF +
## X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath +
## FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual +
## TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea +
## PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch +
## ScreenPorch + PoolArea + MiscVal + MoSold + YrSold + SaleType +
## SaleCondition
##
## Df Sum of Sq RSS AIC
## - Exterior2nd 14 0.1316 15.380 -6249.6
## - RoofStyle 5 0.0403 15.288 -6240.3
## - ExterQual 3 0.0103 15.258 -6239.1
## - Electrical 4 0.0328 15.281 -6239.0
## - MasVnrArea 1 0.0005 15.249 -6236.1
## - BsmtHalfBath 1 0.0020 15.250 -6235.9
## - YrSold 1 0.0038 15.252 -6235.7
## - MasVnrType 3 0.0467 15.295 -6235.7
## - MiscVal 1 0.0057 15.254 -6235.6
## - BedroomAbvGr 1 0.0103 15.258 -6235.1
## - LotShape 3 0.0550 15.303 -6234.9
## - PavedDrive 2 0.0341 15.282 -6234.9
## - MoSold 1 0.0136 15.262 -6234.8
## - Id 1 0.0148 15.263 -6234.7
## - HouseStyle 7 0.1463 15.394 -6234.2
## - MSSubClass 1 0.0198 15.268 -6234.2
## - OpenPorchSF 1 0.0207 15.269 -6234.1
## <none> 15.248 -6234.1
## - PoolArea 1 0.0367 15.285 -6232.6
## - TotRmsAbvGrd 1 0.0383 15.287 -6232.5
## - KitchenAbvGr 1 0.0393 15.287 -6232.4
## - LowQualFinSF 1 0.0462 15.294 -6231.7
## - X3SsnPorch 1 0.0465 15.295 -6231.7
## - ExterCond 4 0.1106 15.359 -6231.6
## - Utilities 1 0.0493 15.297 -6231.4
## - FullBath 1 0.0498 15.298 -6231.4
## - Street 1 0.0552 15.303 -6230.9
## - HalfBath 1 0.0570 15.305 -6230.7
## - EnclosedPorch 1 0.0619 15.310 -6230.2
## - BldgType 4 0.1279 15.376 -6230.0
## - LandContour 3 0.1139 15.362 -6229.3
## - Exterior1st 13 0.3311 15.579 -6228.9
## - HeatingQC 4 0.1449 15.393 -6228.4
## - YearRemodAdd 1 0.0900 15.338 -6227.6
## - GarageArea 1 0.0916 15.340 -6227.4
## - GarageCars 1 0.1068 15.355 -6226.0
## - LandSlope 2 0.1411 15.389 -6224.7
## - CentralAir 1 0.1202 15.368 -6224.7
## - Heating 5 0.2102 15.458 -6224.2
## - LotConfig 4 0.1993 15.447 -6223.3
## - BsmtFinSF2 1 0.1388 15.387 -6223.0
## - BsmtUnfSF 1 0.1538 15.402 -6221.5
## - Foundation 5 0.2515 15.500 -6220.4
## - KitchenQual 3 0.2090 15.457 -6220.4
## - SaleType 8 0.3228 15.571 -6219.7
## - BsmtFullBath 1 0.1805 15.429 -6219.0
## - WoodDeckSF 1 0.1825 15.431 -6218.8
## - Fireplaces 1 0.2265 15.475 -6214.7
## - LotArea 1 0.2276 15.476 -6214.6
## - ScreenPorch 1 0.2944 15.543 -6208.4
## - YearBuilt 1 0.3132 15.561 -6206.6
## - SaleCondition 5 0.4280 15.676 -6203.9
## - Condition1 8 0.6387 15.887 -6190.6
## - BsmtFinSF1 1 0.5015 15.750 -6189.1
## - Functional 6 0.6473 15.895 -6185.8
## - X2ndFlrSF 1 0.7136 15.962 -6169.7
## - MSZoning 4 0.9655 16.214 -6153.0
## - OverallCond 1 1.0408 16.289 -6140.3
## - OverallQual 1 1.1435 16.392 -6131.2
## - X1stFlrSF 1 1.1799 16.428 -6128.0
## - Neighborhood 24 1.9392 17.187 -6108.4
## - RoofMatl 7 3.4112 18.659 -5955.2
##
## Step: AIC=-6249.64
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl +
## Exterior1st + MasVnrType + MasVnrArea + ExterQual + ExterCond +
## Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating +
## HeatingQC + CentralAir + Electrical + X1stFlrSF + X2ndFlrSF +
## LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath +
## BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd +
## Functional + Fireplaces + GarageCars + GarageArea + PavedDrive +
## WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + MiscVal + MoSold + YrSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - RoofStyle 5 0.0427 15.422 -6255.6
## - ExterQual 3 0.0077 15.387 -6254.9
## - Electrical 4 0.0395 15.419 -6253.9
## - MasVnrArea 1 0.0006 15.380 -6251.6
## - BsmtHalfBath 1 0.0022 15.382 -6251.4
## - YrSold 1 0.0028 15.383 -6251.4
## - MasVnrType 3 0.0482 15.428 -6251.1
## - MiscVal 1 0.0061 15.386 -6251.1
## - LotShape 3 0.0487 15.428 -6251.1
## - BedroomAbvGr 1 0.0108 15.390 -6250.6
## - PavedDrive 2 0.0324 15.412 -6250.6
## - MoSold 1 0.0142 15.394 -6250.3
## - Id 1 0.0160 15.396 -6250.1
## <none> 15.380 -6249.6
## - HouseStyle 7 0.1499 15.530 -6249.6
## - MSSubClass 1 0.0222 15.402 -6249.5
## - OpenPorchSF 1 0.0273 15.407 -6249.1
## - TotRmsAbvGrd 1 0.0348 15.415 -6248.4
## - PoolArea 1 0.0362 15.416 -6248.2
## - KitchenAbvGr 1 0.0450 15.425 -6247.4
## - LowQualFinSF 1 0.0482 15.428 -6247.1
## - Street 1 0.0495 15.429 -6247.0
## - X3SsnPorch 1 0.0497 15.429 -6247.0
## - FullBath 1 0.0508 15.431 -6246.9
## - Utilities 1 0.0523 15.432 -6246.7
## - ExterCond 4 0.1169 15.497 -6246.7
## - EnclosedPorch 1 0.0599 15.440 -6246.0
## - HalfBath 1 0.0600 15.440 -6246.0
## - HeatingQC 4 0.1317 15.511 -6245.3
## - LandContour 3 0.1257 15.505 -6243.8
## - BldgType 4 0.1495 15.529 -6243.6
## - YearRemodAdd 1 0.0903 15.470 -6243.1
## - GarageArea 1 0.1025 15.482 -6242.0
## - GarageCars 1 0.1030 15.483 -6241.9
## - Exterior1st 14 0.3837 15.763 -6241.9
## - LandSlope 2 0.1288 15.508 -6241.5
## - Heating 5 0.2111 15.591 -6239.9
## - CentralAir 1 0.1274 15.507 -6239.7
## - LotConfig 4 0.1976 15.577 -6239.1
## - BsmtFinSF2 1 0.1428 15.523 -6238.2
## - BsmtUnfSF 1 0.1537 15.533 -6237.2
## - Foundation 5 0.2413 15.621 -6237.1
## - BsmtFullBath 1 0.1718 15.552 -6235.5
## - SaleType 8 0.3246 15.704 -6235.3
## - KitchenQual 3 0.2195 15.599 -6235.1
## - WoodDeckSF 1 0.1795 15.559 -6234.8
## + Exterior2nd 14 0.1316 15.248 -6234.1
## - LotArea 1 0.1992 15.579 -6233.0
## - Fireplaces 1 0.2271 15.607 -6230.4
## - ScreenPorch 1 0.2898 15.669 -6224.6
## - YearBuilt 1 0.3421 15.722 -6219.7
## - SaleCondition 5 0.4391 15.819 -6218.8
## - Condition1 8 0.6405 16.020 -6206.4
## - BsmtFinSF1 1 0.5053 15.885 -6204.7
## - Functional 6 0.6787 16.058 -6199.0
## - X2ndFlrSF 1 0.7426 16.122 -6183.2
## - MSZoning 4 0.9747 16.354 -6168.5
## - OverallCond 1 1.1019 16.482 -6151.2
## - OverallQual 1 1.1551 16.535 -6146.6
## - X1stFlrSF 1 1.2349 16.615 -6139.6
## - Neighborhood 24 1.9011 17.281 -6128.5
## - RoofMatl 7 3.4778 18.858 -5967.8
##
## Step: AIC=-6255.62
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + MasVnrArea + ExterQual + ExterCond + Foundation +
## BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC +
## CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF +
## BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr +
## KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional +
## Fireplaces + GarageCars + GarageArea + PavedDrive + WoodDeckSF +
## OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + MiscVal + MoSold + YrSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - ExterQual 3 0.0063 15.429 -6261.0
## - Electrical 4 0.0386 15.461 -6260.0
## - MiscVal 1 0.0003 15.423 -6257.6
## - MasVnrArea 1 0.0008 15.423 -6257.5
## - BsmtHalfBath 1 0.0016 15.424 -6257.5
## - YrSold 1 0.0026 15.425 -6257.4
## - PavedDrive 2 0.0239 15.446 -6257.4
## - LotShape 3 0.0496 15.472 -6257.0
## - MasVnrType 3 0.0497 15.472 -6256.9
## - BedroomAbvGr 1 0.0089 15.431 -6256.8
## - Id 1 0.0138 15.436 -6256.3
## - MoSold 1 0.0140 15.436 -6256.3
## <none> 15.422 -6255.6
## - HouseStyle 7 0.1499 15.572 -6255.6
## - OpenPorchSF 1 0.0237 15.446 -6255.4
## - MSSubClass 1 0.0247 15.447 -6255.3
## - PoolArea 1 0.0363 15.459 -6254.2
## - TotRmsAbvGrd 1 0.0365 15.459 -6254.2
## - FullBath 1 0.0450 15.467 -6253.4
## - KitchenAbvGr 1 0.0451 15.467 -6253.4
## - Street 1 0.0485 15.471 -6253.1
## - X3SsnPorch 1 0.0497 15.472 -6252.9
## - LowQualFinSF 1 0.0502 15.473 -6252.9
## - Utilities 1 0.0506 15.473 -6252.9
## - ExterCond 4 0.1216 15.544 -6252.2
## - EnclosedPorch 1 0.0648 15.487 -6251.5
## - HalfBath 1 0.0682 15.491 -6251.2
## - HeatingQC 4 0.1405 15.563 -6250.5
## - BldgType 4 0.1472 15.569 -6249.8
## - LandContour 3 0.1258 15.548 -6249.8
## + RoofStyle 5 0.0427 15.380 -6249.6
## - YearRemodAdd 1 0.0871 15.509 -6249.5
## - LandSlope 2 0.1141 15.536 -6248.9
## - GarageArea 1 0.1031 15.525 -6248.0
## - GarageCars 1 0.1068 15.529 -6247.6
## - Exterior1st 14 0.3903 15.813 -6247.4
## - Heating 5 0.2099 15.632 -6246.0
## - CentralAir 1 0.1246 15.547 -6245.9
## - LotConfig 4 0.1912 15.614 -6245.7
## - BsmtFinSF2 1 0.1569 15.579 -6242.9
## - BsmtUnfSF 1 0.1578 15.580 -6242.9
## - BsmtFullBath 1 0.1659 15.588 -6242.1
## - Foundation 5 0.2571 15.679 -6241.6
## - SaleType 8 0.3257 15.748 -6241.3
## - KitchenQual 3 0.2207 15.643 -6241.0
## - WoodDeckSF 1 0.1854 15.608 -6240.3
## + Exterior2nd 14 0.1339 15.288 -6240.3
## - LotArea 1 0.1862 15.608 -6240.2
## - Fireplaces 1 0.2259 15.648 -6236.5
## - ScreenPorch 1 0.2885 15.711 -6230.7
## - YearBuilt 1 0.3476 15.770 -6225.3
## - SaleCondition 5 0.4521 15.874 -6223.7
## - Condition1 8 0.6417 16.064 -6212.5
## - BsmtFinSF1 1 0.5205 15.943 -6209.5
## - Functional 6 0.6848 16.107 -6204.6
## - X2ndFlrSF 1 0.7832 16.206 -6185.7
## - MSZoning 4 0.9787 16.401 -6174.3
## - OverallCond 1 1.1124 16.535 -6156.6
## - OverallQual 1 1.1656 16.588 -6151.9
## - X1stFlrSF 1 1.2511 16.674 -6144.4
## - Neighborhood 24 1.9022 17.325 -6134.9
## - RoofMatl 7 3.5216 18.944 -5971.2
##
## Step: AIC=-6261.03
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + MasVnrArea + ExterCond + Foundation + BsmtFinSF1 +
## BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC + CentralAir +
## Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath +
## BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr +
## KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageCars +
## GarageArea + PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch +
## X3SsnPorch + ScreenPorch + PoolArea + MiscVal + MoSold +
## YrSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - Electrical 4 0.0381 15.467 -6265.4
## - MiscVal 1 0.0002 15.429 -6263.0
## - PavedDrive 2 0.0224 15.451 -6262.9
## - MasVnrArea 1 0.0012 15.430 -6262.9
## - BsmtHalfBath 1 0.0015 15.430 -6262.9
## - YrSold 1 0.0024 15.431 -6262.8
## - LotShape 3 0.0498 15.479 -6262.3
## - MasVnrType 3 0.0501 15.479 -6262.3
## - BedroomAbvGr 1 0.0088 15.438 -6262.2
## - MoSold 1 0.0137 15.442 -6261.7
## - Id 1 0.0140 15.443 -6261.7
## <none> 15.429 -6261.0
## - OpenPorchSF 1 0.0222 15.451 -6260.9
## - HouseStyle 7 0.1529 15.582 -6260.7
## - MSSubClass 1 0.0299 15.459 -6260.2
## - TotRmsAbvGrd 1 0.0357 15.464 -6259.7
## - PoolArea 1 0.0362 15.465 -6259.6
## - Street 1 0.0435 15.472 -6258.9
## - KitchenAbvGr 1 0.0442 15.473 -6258.9
## - FullBath 1 0.0450 15.474 -6258.8
## - X3SsnPorch 1 0.0492 15.478 -6258.4
## - Utilities 1 0.0509 15.480 -6258.2
## - ExterCond 4 0.1176 15.546 -6258.0
## - LowQualFinSF 1 0.0544 15.483 -6257.9
## - EnclosedPorch 1 0.0657 15.494 -6256.9
## - HalfBath 1 0.0690 15.498 -6256.5
## - HeatingQC 4 0.1410 15.570 -6255.8
## + ExterQual 3 0.0063 15.422 -6255.6
## - LandContour 3 0.1225 15.551 -6255.5
## - YearRemodAdd 1 0.0860 15.515 -6255.0
## + RoofStyle 5 0.0413 15.387 -6254.9
## - BldgType 4 0.1544 15.583 -6254.6
## - LandSlope 2 0.1122 15.541 -6254.5
## - GarageArea 1 0.1033 15.532 -6253.3
## - GarageCars 1 0.1068 15.536 -6253.0
## - Exterior1st 14 0.3918 15.820 -6252.6
## - CentralAir 1 0.1234 15.552 -6251.5
## - Heating 5 0.2115 15.640 -6251.3
## - LotConfig 4 0.1906 15.619 -6251.2
## - BsmtFinSF2 1 0.1587 15.587 -6248.2
## - BsmtUnfSF 1 0.1621 15.591 -6247.9
## - BsmtFullBath 1 0.1655 15.594 -6247.5
## - Foundation 5 0.2532 15.682 -6247.4
## - LotArea 1 0.1821 15.611 -6246.0
## - SaleType 8 0.3336 15.762 -6246.0
## - WoodDeckSF 1 0.1859 15.615 -6245.6
## + Exterior2nd 14 0.1313 15.297 -6245.4
## - KitchenQual 3 0.2370 15.666 -6244.9
## - Fireplaces 1 0.2295 15.658 -6241.6
## - ScreenPorch 1 0.2867 15.715 -6236.3
## - YearBuilt 1 0.3529 15.782 -6230.2
## - SaleCondition 5 0.4520 15.881 -6229.1
## - Condition1 8 0.6390 16.068 -6218.1
## - BsmtFinSF1 1 0.5251 15.954 -6214.5
## - Functional 6 0.6854 16.114 -6210.0
## - X2ndFlrSF 1 0.7972 16.226 -6189.9
## - MSZoning 4 0.9747 16.403 -6180.1
## - OverallCond 1 1.1068 16.535 -6162.5
## - OverallQual 1 1.1900 16.619 -6155.2
## - X1stFlrSF 1 1.2488 16.677 -6150.1
## - Neighborhood 24 1.9390 17.368 -6137.2
## - RoofMatl 7 3.5292 18.958 -5976.1
##
## Step: AIC=-6265.45
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + MasVnrArea + ExterCond + Foundation + BsmtFinSF1 +
## BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC + CentralAir +
## X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath +
## FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual +
## TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea +
## PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch +
## ScreenPorch + PoolArea + MiscVal + MoSold + YrSold + SaleType +
## SaleCondition
##
## Df Sum of Sq RSS AIC
## - PavedDrive 2 0.0211 15.488 -6267.5
## - MiscVal 1 0.0003 15.467 -6267.4
## - MasVnrArea 1 0.0015 15.468 -6267.3
## - BsmtHalfBath 1 0.0018 15.469 -6267.3
## - LotShape 3 0.0455 15.512 -6267.2
## - YrSold 1 0.0030 15.470 -6267.2
## - BedroomAbvGr 1 0.0077 15.474 -6266.7
## - MasVnrType 3 0.0530 15.520 -6266.5
## - MoSold 1 0.0113 15.478 -6266.4
## - Id 1 0.0148 15.482 -6266.1
## <none> 15.467 -6265.4
## - OpenPorchSF 1 0.0214 15.488 -6265.4
## - HouseStyle 7 0.1547 15.621 -6265.0
## - MSSubClass 1 0.0311 15.498 -6264.5
## - PoolArea 1 0.0349 15.502 -6264.2
## - TotRmsAbvGrd 1 0.0377 15.505 -6263.9
## - FullBath 1 0.0417 15.508 -6263.5
## - KitchenAbvGr 1 0.0433 15.510 -6263.4
## - Street 1 0.0435 15.510 -6263.4
## - Utilities 1 0.0452 15.512 -6263.2
## - X3SsnPorch 1 0.0499 15.517 -6262.8
## - LowQualFinSF 1 0.0500 15.517 -6262.8
## - ExterCond 4 0.1171 15.584 -6262.5
## - EnclosedPorch 1 0.0615 15.528 -6261.7
## - HalfBath 1 0.0686 15.535 -6261.0
## + Electrical 4 0.0381 15.429 -6261.0
## - HeatingQC 4 0.1412 15.608 -6260.3
## - YearRemodAdd 1 0.0783 15.545 -6260.1
## + ExterQual 3 0.0058 15.461 -6260.0
## - LandContour 3 0.1291 15.596 -6259.4
## + RoofStyle 5 0.0406 15.426 -6259.3
## - BldgType 4 0.1531 15.620 -6259.2
## - LandSlope 2 0.1132 15.580 -6258.9
## - GarageArea 1 0.1003 15.567 -6258.1
## - GarageCars 1 0.1071 15.574 -6257.4
## - Heating 5 0.2056 15.672 -6256.3
## - Exterior1st 14 0.4090 15.876 -6255.6
## - LotConfig 4 0.1934 15.660 -6255.4
## - CentralAir 1 0.1355 15.602 -6254.8
## - Foundation 5 0.2437 15.710 -6252.8
## - BsmtFinSF2 1 0.1581 15.625 -6252.7
## - BsmtFullBath 1 0.1626 15.629 -6252.3
## - BsmtUnfSF 1 0.1635 15.630 -6252.2
## - SaleType 8 0.3260 15.793 -6251.2
## + Exterior2nd 14 0.1369 15.330 -6250.3
## - WoodDeckSF 1 0.1840 15.651 -6250.3
## - LotArea 1 0.1872 15.654 -6250.0
## - KitchenQual 3 0.2402 15.707 -6249.1
## - Fireplaces 1 0.2210 15.688 -6246.9
## - ScreenPorch 1 0.2842 15.751 -6241.0
## - YearBuilt 1 0.3429 15.810 -6235.6
## - SaleCondition 5 0.4403 15.907 -6234.7
## - Condition1 8 0.6323 16.099 -6223.3
## - BsmtFinSF1 1 0.5286 15.995 -6218.7
## - Functional 6 0.6876 16.154 -6214.3
## - X2ndFlrSF 1 0.8192 16.286 -6192.6
## - MSZoning 4 0.9984 16.465 -6182.7
## - OverallCond 1 1.0794 16.546 -6169.6
## - OverallQual 1 1.1915 16.658 -6159.8
## - X1stFlrSF 1 1.2623 16.729 -6153.6
## - Neighborhood 24 1.9418 17.409 -6141.8
## - RoofMatl 7 3.5280 18.995 -5981.3
##
## Step: AIC=-6267.47
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + MasVnrArea + ExterCond + Foundation + BsmtFinSF1 +
## BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC + CentralAir +
## X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath +
## FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual +
## TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea +
## WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + MiscVal + MoSold + YrSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - MiscVal 1 0.0005 15.488 -6269.4
## - MasVnrArea 1 0.0019 15.490 -6269.3
## - BsmtHalfBath 1 0.0020 15.490 -6269.3
## - YrSold 1 0.0028 15.491 -6269.2
## - LotShape 3 0.0466 15.534 -6269.1
## - BedroomAbvGr 1 0.0076 15.495 -6268.8
## - MoSold 1 0.0109 15.499 -6268.5
## - MasVnrType 3 0.0540 15.542 -6268.4
## - Id 1 0.0148 15.503 -6268.1
## - OpenPorchSF 1 0.0203 15.508 -6267.6
## <none> 15.488 -6267.5
## - HouseStyle 7 0.1556 15.643 -6267.0
## - MSSubClass 1 0.0300 15.518 -6266.7
## - PoolArea 1 0.0346 15.522 -6266.2
## - TotRmsAbvGrd 1 0.0351 15.523 -6266.2
## - FullBath 1 0.0407 15.529 -6265.7
## + PavedDrive 2 0.0211 15.467 -6265.4
## - Street 1 0.0442 15.532 -6265.3
## - Utilities 1 0.0447 15.533 -6265.3
## - KitchenAbvGr 1 0.0478 15.536 -6265.0
## - X3SsnPorch 1 0.0486 15.537 -6264.9
## - LowQualFinSF 1 0.0520 15.540 -6264.6
## - ExterCond 4 0.1166 15.604 -6264.6
## - EnclosedPorch 1 0.0599 15.548 -6263.9
## - HalfBath 1 0.0678 15.556 -6263.1
## + Electrical 4 0.0367 15.451 -6262.9
## - YearRemodAdd 1 0.0719 15.560 -6262.7
## - HeatingQC 4 0.1410 15.629 -6262.3
## + ExterQual 3 0.0045 15.483 -6261.9
## - BldgType 4 0.1525 15.640 -6261.3
## - LandSlope 2 0.1111 15.599 -6261.1
## - LandContour 3 0.1362 15.624 -6260.8
## + RoofStyle 5 0.0332 15.455 -6260.6
## - GarageCars 1 0.1049 15.593 -6259.7
## - GarageArea 1 0.1101 15.598 -6259.2
## - Heating 5 0.2031 15.691 -6258.6
## - LotConfig 4 0.1943 15.682 -6257.4
## - Exterior1st 14 0.4175 15.905 -6256.9
## - CentralAir 1 0.1410 15.629 -6256.3
## - BsmtFullBath 1 0.1586 15.646 -6254.7
## - Foundation 5 0.2460 15.734 -6254.6
## - BsmtFinSF2 1 0.1613 15.649 -6254.4
## - BsmtUnfSF 1 0.1644 15.652 -6254.1
## - SaleType 8 0.3216 15.809 -6253.6
## - WoodDeckSF 1 0.1840 15.672 -6252.3
## - LotArea 1 0.1860 15.674 -6252.1
## + Exterior2nd 14 0.1344 15.354 -6252.1
## - KitchenQual 3 0.2381 15.726 -6251.3
## - Fireplaces 1 0.2274 15.715 -6248.3
## - ScreenPorch 1 0.2898 15.778 -6242.6
## - SaleCondition 5 0.4375 15.925 -6237.0
## - YearBuilt 1 0.3886 15.876 -6233.5
## - Condition1 8 0.6425 16.130 -6224.5
## - BsmtFinSF1 1 0.5343 16.022 -6220.3
## - Functional 6 0.7038 16.192 -6215.0
## - X2ndFlrSF 1 0.8294 16.317 -6193.8
## - MSZoning 4 1.0046 16.492 -6184.3
## - OverallCond 1 1.0961 16.584 -6170.2
## - OverallQual 1 1.1857 16.674 -6162.4
## - X1stFlrSF 1 1.2679 16.756 -6155.3
## - Neighborhood 24 1.9571 17.445 -6142.8
## - RoofMatl 7 3.5388 19.027 -5982.9
##
## Step: AIC=-6269.42
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + MasVnrArea + ExterCond + Foundation + BsmtFinSF1 +
## BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC + CentralAir +
## X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath +
## FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual +
## TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea +
## WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + MoSold + YrSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - MasVnrArea 1 0.0018 15.490 -6271.2
## - BsmtHalfBath 1 0.0021 15.490 -6271.2
## - YrSold 1 0.0028 15.491 -6271.2
## - LotShape 3 0.0471 15.535 -6271.0
## - BedroomAbvGr 1 0.0079 15.496 -6270.7
## - MoSold 1 0.0109 15.499 -6270.4
## - MasVnrType 3 0.0544 15.543 -6270.3
## - Id 1 0.0148 15.503 -6270.0
## - OpenPorchSF 1 0.0204 15.509 -6269.5
## <none> 15.488 -6269.4
## - HouseStyle 7 0.1555 15.644 -6268.9
## - MSSubClass 1 0.0299 15.518 -6268.6
## - PoolArea 1 0.0344 15.523 -6268.2
## - TotRmsAbvGrd 1 0.0347 15.523 -6268.2
## - FullBath 1 0.0407 15.529 -6267.6
## + MiscVal 1 0.0005 15.488 -6267.5
## + PavedDrive 2 0.0213 15.467 -6267.4
## - Street 1 0.0445 15.533 -6267.3
## - Utilities 1 0.0448 15.533 -6267.2
## - KitchenAbvGr 1 0.0481 15.537 -6266.9
## - X3SsnPorch 1 0.0485 15.537 -6266.9
## - LowQualFinSF 1 0.0522 15.540 -6266.5
## - ExterCond 4 0.1178 15.606 -6266.4
## - EnclosedPorch 1 0.0595 15.548 -6265.9
## - HalfBath 1 0.0677 15.556 -6265.1
## + Electrical 4 0.0368 15.452 -6264.9
## - YearRemodAdd 1 0.0716 15.560 -6264.7
## - HeatingQC 4 0.1411 15.629 -6264.3
## + ExterQual 3 0.0043 15.484 -6263.8
## - BldgType 4 0.1526 15.641 -6263.2
## - LandSlope 2 0.1111 15.600 -6263.1
## - LandContour 3 0.1361 15.624 -6262.7
## + RoofStyle 5 0.0279 15.460 -6262.0
## - GarageCars 1 0.1052 15.594 -6261.6
## - GarageArea 1 0.1100 15.598 -6261.2
## - Heating 5 0.2032 15.692 -6260.5
## - LotConfig 4 0.1938 15.682 -6259.4
## - Exterior1st 14 0.4175 15.906 -6258.8
## - CentralAir 1 0.1412 15.630 -6258.3
## - Foundation 5 0.2458 15.734 -6256.6
## - BsmtFullBath 1 0.1596 15.648 -6256.5
## - BsmtFinSF2 1 0.1609 15.649 -6256.4
## - BsmtUnfSF 1 0.1639 15.652 -6256.1
## - SaleType 8 0.3222 15.811 -6255.5
## - WoodDeckSF 1 0.1841 15.672 -6254.3
## - LotArea 1 0.1856 15.674 -6254.1
## + Exterior2nd 14 0.1346 15.354 -6254.1
## - KitchenQual 3 0.2388 15.727 -6253.2
## - Fireplaces 1 0.2271 15.716 -6250.3
## - ScreenPorch 1 0.2893 15.778 -6244.6
## - SaleCondition 5 0.4375 15.926 -6239.0
## - YearBuilt 1 0.3881 15.876 -6235.5
## - Condition1 8 0.6427 16.131 -6226.4
## - BsmtFinSF1 1 0.5341 16.023 -6222.2
## - Functional 6 0.7068 16.195 -6216.7
## - X2ndFlrSF 1 0.8289 16.317 -6195.8
## - MSZoning 4 1.0047 16.493 -6186.2
## - OverallCond 1 1.0965 16.585 -6172.2
## - OverallQual 1 1.1853 16.674 -6164.4
## - X1stFlrSF 1 1.2777 16.766 -6156.4
## - Neighborhood 24 1.9594 17.448 -6144.6
## - RoofMatl 7 3.5386 19.027 -5984.8
##
## Step: AIC=-6271.25
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 +
## BsmtUnfSF + Heating + HeatingQC + CentralAir + X1stFlrSF +
## X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath +
## FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual +
## TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea +
## WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + MoSold + YrSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - BsmtHalfBath 1 0.0020 15.492 -6273.1
## - YrSold 1 0.0027 15.493 -6273.0
## - LotShape 3 0.0468 15.537 -6272.9
## - BedroomAbvGr 1 0.0082 15.498 -6272.5
## - MasVnrType 3 0.0529 15.543 -6272.3
## - MoSold 1 0.0105 15.501 -6272.3
## - Id 1 0.0145 15.505 -6271.9
## <none> 15.490 -6271.2
## - OpenPorchSF 1 0.0214 15.512 -6271.2
## - HouseStyle 7 0.1564 15.647 -6270.7
## - MSSubClass 1 0.0303 15.521 -6270.4
## - TotRmsAbvGrd 1 0.0352 15.525 -6270.0
## - PoolArea 1 0.0358 15.526 -6269.9
## - FullBath 1 0.0409 15.531 -6269.4
## + MasVnrArea 1 0.0018 15.488 -6269.4
## + MiscVal 1 0.0005 15.490 -6269.3
## + PavedDrive 2 0.0217 15.469 -6269.3
## - Street 1 0.0438 15.534 -6269.2
## - Utilities 1 0.0469 15.537 -6268.9
## - KitchenAbvGr 1 0.0484 15.539 -6268.7
## - X3SsnPorch 1 0.0488 15.539 -6268.7
## - LowQualFinSF 1 0.0520 15.542 -6268.4
## - ExterCond 4 0.1186 15.609 -6268.2
## - EnclosedPorch 1 0.0601 15.550 -6267.6
## - HalfBath 1 0.0671 15.557 -6267.0
## + Electrical 4 0.0371 15.453 -6266.7
## - YearRemodAdd 1 0.0722 15.562 -6266.5
## - HeatingQC 4 0.1409 15.631 -6266.1
## + ExterQual 3 0.0049 15.485 -6265.7
## - BldgType 4 0.1522 15.642 -6265.1
## - LandSlope 2 0.1105 15.601 -6264.9
## - LandContour 3 0.1360 15.626 -6264.6
## + RoofStyle 5 0.0280 15.462 -6263.9
## - GarageCars 1 0.1051 15.595 -6263.4
## - GarageArea 1 0.1094 15.600 -6263.0
## - Heating 5 0.2044 15.695 -6262.2
## - LotConfig 4 0.1928 15.683 -6261.3
## - Exterior1st 14 0.4177 15.908 -6260.6
## - CentralAir 1 0.1422 15.633 -6260.0
## - BsmtFinSF2 1 0.1596 15.650 -6258.4
## - Foundation 5 0.2473 15.738 -6258.3
## - BsmtUnfSF 1 0.1623 15.652 -6258.1
## - BsmtFullBath 1 0.1625 15.653 -6258.1
## - SaleType 8 0.3220 15.812 -6257.4
## - WoodDeckSF 1 0.1837 15.674 -6256.1
## - LotArea 1 0.1840 15.674 -6256.1
## + Exterior2nd 14 0.1348 15.355 -6255.9
## - KitchenQual 3 0.2372 15.727 -6255.2
## - Fireplaces 1 0.2266 15.717 -6252.2
## - ScreenPorch 1 0.2883 15.778 -6246.5
## - SaleCondition 5 0.4357 15.926 -6241.0
## - YearBuilt 1 0.3884 15.879 -6237.3
## - Condition1 8 0.6445 16.135 -6228.1
## - BsmtFinSF1 1 0.5335 16.024 -6224.1
## - Functional 6 0.7051 16.195 -6218.7
## - X2ndFlrSF 1 0.8315 16.322 -6197.4
## - MSZoning 4 1.0046 16.495 -6188.1
## - OverallCond 1 1.0965 16.587 -6174.0
## - OverallQual 1 1.1840 16.674 -6166.4
## - X1stFlrSF 1 1.2760 16.766 -6158.4
## - Neighborhood 24 1.9620 17.452 -6146.2
## - RoofMatl 7 3.5391 19.029 -5986.7
##
## Step: AIC=-6273.06
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 +
## BsmtUnfSF + Heating + HeatingQC + CentralAir + X1stFlrSF +
## X2ndFlrSF + LowQualFinSF + BsmtFullBath + FullBath + HalfBath +
## BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd +
## Functional + Fireplaces + GarageCars + GarageArea + WoodDeckSF +
## OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + MoSold + YrSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - YrSold 1 0.0029 15.495 -6274.8
## - LotShape 3 0.0485 15.541 -6274.5
## - BedroomAbvGr 1 0.0088 15.501 -6274.2
## - MasVnrType 3 0.0523 15.545 -6274.2
## - MoSold 1 0.0103 15.502 -6274.1
## - Id 1 0.0148 15.507 -6273.7
## <none> 15.492 -6273.1
## - OpenPorchSF 1 0.0214 15.514 -6273.1
## - HouseStyle 7 0.1594 15.652 -6272.2
## - MSSubClass 1 0.0309 15.523 -6272.2
## - TotRmsAbvGrd 1 0.0350 15.527 -6271.8
## - PoolArea 1 0.0356 15.528 -6271.7
## - FullBath 1 0.0395 15.532 -6271.4
## + BsmtHalfBath 1 0.0020 15.490 -6271.2
## + MasVnrArea 1 0.0018 15.490 -6271.2
## + MiscVal 1 0.0006 15.492 -6271.1
## + PavedDrive 2 0.0218 15.470 -6271.1
## - Street 1 0.0442 15.536 -6270.9
## - Utilities 1 0.0456 15.538 -6270.8
## - KitchenAbvGr 1 0.0487 15.541 -6270.5
## - X3SsnPorch 1 0.0499 15.542 -6270.4
## - LowQualFinSF 1 0.0523 15.545 -6270.2
## - ExterCond 4 0.1188 15.611 -6270.0
## - EnclosedPorch 1 0.0609 15.553 -6269.4
## - HalfBath 1 0.0664 15.559 -6268.9
## + Electrical 4 0.0374 15.455 -6268.6
## - YearRemodAdd 1 0.0735 15.566 -6268.2
## - HeatingQC 4 0.1414 15.634 -6267.9
## + ExterQual 3 0.0048 15.488 -6267.5
## - BldgType 4 0.1522 15.645 -6266.9
## - LandSlope 2 0.1095 15.602 -6266.8
## - LandContour 3 0.1391 15.631 -6266.1
## + RoofStyle 5 0.0273 15.465 -6265.6
## - GarageCars 1 0.1052 15.597 -6265.2
## - GarageArea 1 0.1100 15.602 -6264.8
## - Heating 5 0.2054 15.698 -6263.9
## - LotConfig 4 0.1921 15.684 -6263.2
## - Exterior1st 14 0.4175 15.910 -6262.5
## - CentralAir 1 0.1427 15.635 -6261.8
## - Foundation 5 0.2472 15.739 -6260.1
## - BsmtUnfSF 1 0.1634 15.656 -6259.8
## - BsmtFinSF2 1 0.1663 15.659 -6259.6
## - BsmtFullBath 1 0.1679 15.660 -6259.4
## - SaleType 8 0.3233 15.816 -6259.1
## - LotArea 1 0.1829 15.675 -6258.0
## - WoodDeckSF 1 0.1856 15.678 -6257.8
## + Exterior2nd 14 0.1351 15.357 -6257.8
## - KitchenQual 3 0.2380 15.730 -6256.9
## - Fireplaces 1 0.2263 15.719 -6254.0
## - ScreenPorch 1 0.2877 15.780 -6248.4
## - SaleCondition 5 0.4348 15.927 -6242.9
## - YearBuilt 1 0.3888 15.881 -6239.1
## - Condition1 8 0.6465 16.139 -6229.7
## - BsmtFinSF1 1 0.5602 16.052 -6223.5
## - Functional 6 0.7052 16.197 -6220.5
## - X2ndFlrSF 1 0.8311 16.323 -6199.2
## - MSZoning 4 1.0027 16.495 -6190.1
## - OverallCond 1 1.1026 16.595 -6175.3
## - OverallQual 1 1.1821 16.674 -6168.4
## - X1stFlrSF 1 1.2741 16.766 -6160.4
## - Neighborhood 24 1.9601 17.452 -6148.2
## - RoofMatl 7 3.5670 19.059 -5986.4
##
## Step: AIC=-6274.79
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st +
## MasVnrType + ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 +
## BsmtUnfSF + Heating + HeatingQC + CentralAir + X1stFlrSF +
## X2ndFlrSF + LowQualFinSF + BsmtFullBath + FullBath + HalfBath +
## BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd +
## Functional + Fireplaces + GarageCars + GarageArea + WoodDeckSF +
## OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + MoSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - LotShape 3 0.0485 15.544 -6276.3
## - MasVnrType 3 0.0508 15.546 -6276.0
## - BedroomAbvGr 1 0.0090 15.504 -6275.9
## - MoSold 1 0.0091 15.504 -6275.9
## - Id 1 0.0149 15.510 -6275.4
## <none> 15.495 -6274.8
## - OpenPorchSF 1 0.0226 15.518 -6274.7
## - MSSubClass 1 0.0304 15.525 -6273.9
## - HouseStyle 7 0.1595 15.655 -6273.9
## - TotRmsAbvGrd 1 0.0354 15.530 -6273.5
## - PoolArea 1 0.0371 15.532 -6273.3
## - FullBath 1 0.0390 15.534 -6273.1
## + YrSold 1 0.0029 15.492 -6273.1
## + BsmtHalfBath 1 0.0022 15.493 -6273.0
## + MasVnrArea 1 0.0017 15.493 -6273.0
## + MiscVal 1 0.0005 15.495 -6272.8
## + PavedDrive 2 0.0217 15.473 -6272.8
## - Street 1 0.0450 15.540 -6272.6
## - Utilities 1 0.0459 15.541 -6272.5
## - X3SsnPorch 1 0.0497 15.545 -6272.1
## - KitchenAbvGr 1 0.0513 15.546 -6272.0
## - LowQualFinSF 1 0.0532 15.548 -6271.8
## - ExterCond 4 0.1196 15.615 -6271.6
## - EnclosedPorch 1 0.0612 15.556 -6271.1
## - HalfBath 1 0.0659 15.561 -6270.6
## + Electrical 4 0.0380 15.457 -6270.3
## - YearRemodAdd 1 0.0718 15.567 -6270.1
## - HeatingQC 4 0.1416 15.637 -6269.6
## + ExterQual 3 0.0047 15.491 -6269.2
## - BldgType 4 0.1514 15.646 -6268.7
## - LandSlope 2 0.1113 15.606 -6268.4
## - LandContour 3 0.1390 15.634 -6267.8
## + RoofStyle 5 0.0273 15.468 -6267.3
## - GarageCars 1 0.1057 15.601 -6266.9
## - GarageArea 1 0.1102 15.605 -6266.5
## - Heating 5 0.2079 15.703 -6265.4
## - LotConfig 4 0.1910 15.686 -6265.0
## - Exterior1st 14 0.4160 15.911 -6264.3
## - CentralAir 1 0.1433 15.639 -6263.4
## - Foundation 5 0.2464 15.742 -6261.9
## - BsmtUnfSF 1 0.1627 15.658 -6261.6
## - BsmtFinSF2 1 0.1653 15.660 -6261.4
## - BsmtFullBath 1 0.1658 15.661 -6261.4
## - SaleType 8 0.3237 15.819 -6260.8
## - LotArea 1 0.1834 15.678 -6259.7
## - WoodDeckSF 1 0.1852 15.680 -6259.5
## + Exterior2nd 14 0.1343 15.361 -6259.4
## - KitchenQual 3 0.2364 15.732 -6258.8
## - Fireplaces 1 0.2265 15.722 -6255.7
## - ScreenPorch 1 0.2864 15.782 -6250.2
## - SaleCondition 5 0.4321 15.927 -6244.9
## - YearBuilt 1 0.3910 15.886 -6240.6
## - Condition1 8 0.6524 16.148 -6231.0
## - BsmtFinSF1 1 0.5606 16.056 -6225.2
## - Functional 6 0.7122 16.207 -6221.6
## - X2ndFlrSF 1 0.8324 16.328 -6200.9
## - MSZoning 4 1.0105 16.506 -6191.1
## - OverallCond 1 1.1007 16.596 -6177.2
## - OverallQual 1 1.1802 16.675 -6170.3
## - X1stFlrSF 1 1.2789 16.774 -6161.7
## - Neighborhood 24 1.9618 17.457 -6149.8
## - RoofMatl 7 3.5887 19.084 -5986.5
##
## Step: AIC=-6276.26
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LandContour + Utilities + LotConfig + LandSlope + Neighborhood +
## Condition1 + BldgType + HouseStyle + OverallQual + OverallCond +
## YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + MasVnrType +
## ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF +
## Heating + HeatingQC + CentralAir + X1stFlrSF + X2ndFlrSF +
## LowQualFinSF + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr +
## KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional +
## Fireplaces + GarageCars + GarageArea + WoodDeckSF + OpenPorchSF +
## EnclosedPorch + X3SsnPorch + ScreenPorch + PoolArea + MoSold +
## SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - MasVnrType 3 0.0458 15.589 -6278.0
## - MoSold 1 0.0092 15.553 -6277.4
## - BedroomAbvGr 1 0.0092 15.553 -6277.4
## - Id 1 0.0145 15.558 -6276.9
## <none> 15.544 -6276.3
## - OpenPorchSF 1 0.0218 15.565 -6276.2
## - HouseStyle 7 0.1537 15.697 -6276.0
## - MSSubClass 1 0.0324 15.576 -6275.2
## - TotRmsAbvGrd 1 0.0342 15.578 -6275.1
## - PoolArea 1 0.0358 15.579 -6274.9
## + LotShape 3 0.0485 15.495 -6274.8
## + BsmtHalfBath 1 0.0039 15.540 -6274.6
## - FullBath 1 0.0391 15.583 -6274.6
## + YrSold 1 0.0028 15.541 -6274.5
## + PavedDrive 2 0.0229 15.521 -6274.4
## + MasVnrArea 1 0.0015 15.542 -6274.4
## + MiscVal 1 0.0010 15.543 -6274.4
## - Street 1 0.0462 15.590 -6273.9
## - Utilities 1 0.0475 15.591 -6273.8
## - X3SsnPorch 1 0.0480 15.592 -6273.8
## - KitchenAbvGr 1 0.0524 15.596 -6273.4
## - LowQualFinSF 1 0.0535 15.597 -6273.3
## - ExterCond 4 0.1201 15.664 -6273.1
## - EnclosedPorch 1 0.0578 15.601 -6272.9
## - HalfBath 1 0.0645 15.608 -6272.2
## + Electrical 4 0.0334 15.510 -6271.4
## - YearRemodAdd 1 0.0780 15.622 -6271.0
## - HeatingQC 4 0.1442 15.688 -6270.9
## - BldgType 4 0.1460 15.690 -6270.7
## + ExterQual 3 0.0039 15.540 -6270.6
## - LandContour 3 0.1361 15.680 -6269.6
## - LandSlope 2 0.1145 15.658 -6269.6
## + RoofStyle 5 0.0265 15.517 -6268.7
## - GarageArea 1 0.1060 15.650 -6268.4
## - GarageCars 1 0.1113 15.655 -6267.9
## - Heating 5 0.2080 15.752 -6267.0
## - Exterior1st 14 0.4184 15.962 -6265.7
## - CentralAir 1 0.1394 15.683 -6265.3
## - LotConfig 4 0.2138 15.757 -6264.4
## - BsmtFullBath 1 0.1565 15.700 -6263.7
## - Foundation 5 0.2440 15.787 -6263.7
## - BsmtUnfSF 1 0.1574 15.701 -6263.6
## - SaleType 8 0.3243 15.868 -6262.3
## - BsmtFinSF2 1 0.1728 15.716 -6262.2
## - WoodDeckSF 1 0.1785 15.722 -6261.7
## + Exterior2nd 14 0.1286 15.415 -6260.3
## - KitchenQual 3 0.2376 15.781 -6260.2
## - Fireplaces 1 0.2269 15.771 -6257.2
## - LotArea 1 0.2476 15.791 -6255.3
## - ScreenPorch 1 0.2980 15.842 -6250.7
## - SaleCondition 5 0.4255 15.969 -6247.1
## - YearBuilt 1 0.3932 15.937 -6242.0
## - Condition1 8 0.6310 16.175 -6234.5
## - BsmtFinSF1 1 0.5606 16.104 -6226.8
## - Functional 6 0.7178 16.261 -6222.7
## - X2ndFlrSF 1 0.8388 16.382 -6202.0
## - MSZoning 4 1.0170 16.561 -6192.3
## - OverallCond 1 1.0965 16.640 -6179.3
## - OverallQual 1 1.1891 16.733 -6171.3
## - X1stFlrSF 1 1.2799 16.823 -6163.4
## - Neighborhood 24 1.9561 17.500 -6152.3
## - RoofMatl 7 3.6904 19.234 -5981.2
##
## Step: AIC=-6277.99
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LandContour + Utilities + LotConfig + LandSlope + Neighborhood +
## Condition1 + BldgType + HouseStyle + OverallQual + OverallCond +
## YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + ExterCond +
## Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating +
## HeatingQC + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF +
## BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr +
## KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageCars +
## GarageArea + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch +
## ScreenPorch + PoolArea + MoSold + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - MoSold 1 0.0090 15.598 -6279.1
## - BedroomAbvGr 1 0.0092 15.599 -6279.1
## - Id 1 0.0137 15.603 -6278.7
## <none> 15.589 -6278.0
## - OpenPorchSF 1 0.0217 15.611 -6278.0
## - HouseStyle 7 0.1539 15.743 -6277.7
## - PoolArea 1 0.0338 15.623 -6276.9
## - MSSubClass 1 0.0344 15.624 -6276.8
## - TotRmsAbvGrd 1 0.0374 15.627 -6276.5
## - FullBath 1 0.0386 15.628 -6276.4
## + MasVnrType 3 0.0458 15.544 -6276.3
## + BsmtHalfBath 1 0.0029 15.586 -6276.3
## + PavedDrive 2 0.0236 15.566 -6276.2
## + MiscVal 1 0.0016 15.588 -6276.1
## + YrSold 1 0.0015 15.588 -6276.1
## + LotShape 3 0.0434 15.546 -6276.0
## + MasVnrArea 1 0.0002 15.589 -6276.0
## - Street 1 0.0462 15.636 -6275.7
## - Utilities 1 0.0468 15.636 -6275.6
## - X3SsnPorch 1 0.0513 15.641 -6275.2
## - KitchenAbvGr 1 0.0536 15.643 -6275.0
## - LowQualFinSF 1 0.0541 15.643 -6275.0
## - ExterCond 4 0.1203 15.710 -6274.8
## - EnclosedPorch 1 0.0610 15.650 -6274.3
## - HalfBath 1 0.0624 15.652 -6274.2
## - BldgType 4 0.1358 15.725 -6273.4
## + Electrical 4 0.0357 15.554 -6273.3
## - YearRemodAdd 1 0.0747 15.664 -6273.1
## + ExterQual 3 0.0036 15.586 -6272.3
## - HeatingQC 4 0.1523 15.742 -6271.9
## - LandSlope 2 0.1144 15.704 -6271.4
## - LandContour 3 0.1426 15.732 -6270.8
## - GarageArea 1 0.1022 15.692 -6270.5
## + RoofStyle 5 0.0269 15.562 -6270.5
## - GarageCars 1 0.1206 15.710 -6268.8
## - Heating 5 0.2077 15.797 -6268.8
## - Exterior1st 14 0.4091 15.998 -6268.4
## - CentralAir 1 0.1356 15.725 -6267.4
## - LotConfig 4 0.2088 15.798 -6266.7
## - Foundation 5 0.2412 15.831 -6265.7
## - BsmtUnfSF 1 0.1556 15.745 -6265.6
## - BsmtFullBath 1 0.1561 15.745 -6265.5
## - BsmtFinSF2 1 0.1643 15.754 -6264.8
## - SaleType 8 0.3235 15.913 -6264.2
## - WoodDeckSF 1 0.1837 15.773 -6263.0
## - KitchenQual 3 0.2341 15.823 -6262.4
## + Exterior2nd 14 0.1313 15.458 -6262.3
## - Fireplaces 1 0.2328 15.822 -6258.5
## - LotArea 1 0.2332 15.823 -6258.4
## - ScreenPorch 1 0.3069 15.896 -6251.7
## - SaleCondition 5 0.4297 16.019 -6248.5
## - YearBuilt 1 0.4059 15.995 -6242.7
## - Condition1 8 0.6357 16.225 -6236.0
## - BsmtFinSF1 1 0.5715 16.161 -6227.7
## - Functional 6 0.7447 16.334 -6222.3
## - X2ndFlrSF 1 0.8429 16.432 -6203.6
## - MSZoning 4 0.9999 16.589 -6195.8
## - OverallCond 1 1.0956 16.685 -6181.4
## - OverallQual 1 1.2502 16.840 -6168.1
## - X1stFlrSF 1 1.2940 16.883 -6164.3
## - Neighborhood 24 1.9849 17.574 -6152.1
## - RoofMatl 7 3.6675 19.257 -5985.4
##
## Step: AIC=-6279.15
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LandContour + Utilities + LotConfig + LandSlope + Neighborhood +
## Condition1 + BldgType + HouseStyle + OverallQual + OverallCond +
## YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + ExterCond +
## Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating +
## HeatingQC + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF +
## BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr +
## KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageCars +
## GarageArea + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch +
## ScreenPorch + PoolArea + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - BedroomAbvGr 1 0.0082 15.607 -6280.4
## - Id 1 0.0143 15.613 -6279.8
## - OpenPorchSF 1 0.0199 15.618 -6279.3
## <none> 15.598 -6279.1
## - HouseStyle 7 0.1571 15.755 -6278.6
## + MoSold 1 0.0090 15.589 -6278.0
## - PoolArea 1 0.0346 15.633 -6277.9
## - MSSubClass 1 0.0373 15.636 -6277.7
## - FullBath 1 0.0385 15.637 -6277.6
## - TotRmsAbvGrd 1 0.0400 15.638 -6277.4
## + MasVnrType 3 0.0457 15.553 -6277.4
## + BsmtHalfBath 1 0.0025 15.596 -6277.4
## + PavedDrive 2 0.0232 15.575 -6277.3
## + MiscVal 1 0.0016 15.597 -6277.3
## + YrSold 1 0.0007 15.598 -6277.2
## + LotShape 3 0.0436 15.555 -6277.2
## + MasVnrArea 1 0.0002 15.598 -6277.2
## - Utilities 1 0.0450 15.643 -6277.0
## - Street 1 0.0463 15.645 -6276.8
## - X3SsnPorch 1 0.0500 15.649 -6276.5
## - LowQualFinSF 1 0.0539 15.652 -6276.1
## - ExterCond 4 0.1192 15.718 -6276.1
## - KitchenAbvGr 1 0.0559 15.654 -6276.0
## - EnclosedPorch 1 0.0630 15.661 -6275.3
## - HalfBath 1 0.0645 15.663 -6275.2
## + Electrical 4 0.0335 15.565 -6274.3
## - YearRemodAdd 1 0.0751 15.674 -6274.2
## - BldgType 4 0.1417 15.740 -6274.0
## + ExterQual 3 0.0036 15.595 -6273.5
## - HeatingQC 4 0.1539 15.752 -6272.9
## - LandSlope 2 0.1168 15.715 -6272.3
## - LandContour 3 0.1413 15.740 -6272.1
## + RoofStyle 5 0.0270 15.572 -6271.7
## - GarageArea 1 0.1039 15.702 -6271.5
## - Heating 5 0.2064 15.805 -6270.1
## - GarageCars 1 0.1199 15.718 -6270.0
## - Exterior1st 14 0.4099 16.008 -6269.5
## - CentralAir 1 0.1350 15.733 -6268.6
## - LotConfig 4 0.2093 15.808 -6267.8
## - Foundation 5 0.2430 15.841 -6266.7
## - BsmtFullBath 1 0.1570 15.755 -6266.6
## - BsmtUnfSF 1 0.1598 15.758 -6266.4
## - BsmtFinSF2 1 0.1666 15.765 -6265.7
## - SaleType 8 0.3208 15.919 -6265.6
## - WoodDeckSF 1 0.1818 15.780 -6264.3
## + Exterior2nd 14 0.1320 15.466 -6263.5
## - KitchenQual 3 0.2362 15.835 -6263.3
## - Fireplaces 1 0.2294 15.828 -6260.0
## - LotArea 1 0.2345 15.833 -6259.5
## - ScreenPorch 1 0.3057 15.904 -6253.0
## - SaleCondition 5 0.4291 16.027 -6249.8
## - YearBuilt 1 0.4061 16.005 -6243.9
## - Condition1 8 0.6299 16.228 -6237.7
## - BsmtFinSF1 1 0.5787 16.177 -6228.3
## - Functional 6 0.7451 16.343 -6223.4
## - X2ndFlrSF 1 0.8388 16.437 -6205.1
## - MSZoning 4 1.0135 16.612 -6195.8
## - OverallCond 1 1.1021 16.701 -6182.1
## - OverallQual 1 1.2424 16.841 -6169.9
## - X1stFlrSF 1 1.2895 16.888 -6165.9
## - Neighborhood 24 1.9764 17.575 -6154.0
## - RoofMatl 7 3.6625 19.261 -5987.1
##
## Step: AIC=-6280.38
## logSalePrice ~ Id + MSSubClass + MSZoning + LotArea + Street +
## LandContour + Utilities + LotConfig + LandSlope + Neighborhood +
## Condition1 + BldgType + HouseStyle + OverallQual + OverallCond +
## YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + ExterCond +
## Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating +
## HeatingQC + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF +
## BsmtFullBath + FullBath + HalfBath + KitchenAbvGr + KitchenQual +
## TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea +
## WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - Id 1 0.0139 15.620 -6281.1
## - OpenPorchSF 1 0.0190 15.626 -6280.6
## <none> 15.607 -6280.4
## - HouseStyle 7 0.1529 15.760 -6280.2
## + BedroomAbvGr 1 0.0082 15.598 -6279.1
## + MoSold 1 0.0081 15.599 -6279.1
## - PoolArea 1 0.0356 15.642 -6279.1
## - MSSubClass 1 0.0362 15.643 -6279.0
## + BsmtHalfBath 1 0.0033 15.603 -6278.7
## + MasVnrType 3 0.0457 15.561 -6278.6
## + MiscVal 1 0.0021 15.605 -6278.6
## + PavedDrive 2 0.0233 15.583 -6278.6
## + YrSold 1 0.0008 15.606 -6278.5
## + LotShape 3 0.0437 15.563 -6278.4
## - FullBath 1 0.0428 15.649 -6278.4
## + MasVnrArea 1 0.0002 15.607 -6278.4
## - Utilities 1 0.0445 15.651 -6278.2
## - Street 1 0.0453 15.652 -6278.2
## - X3SsnPorch 1 0.0494 15.656 -6277.8
## - ExterCond 4 0.1159 15.723 -6277.6
## - LowQualFinSF 1 0.0533 15.660 -6277.4
## - HalfBath 1 0.0621 15.669 -6276.6
## - KitchenAbvGr 1 0.0632 15.670 -6276.5
## - EnclosedPorch 1 0.0651 15.672 -6276.3
## - TotRmsAbvGrd 1 0.0696 15.676 -6275.9
## - YearRemodAdd 1 0.0721 15.679 -6275.7
## + Electrical 4 0.0323 15.574 -6275.4
## + ExterQual 3 0.0034 15.603 -6274.7
## - BldgType 4 0.1495 15.756 -6274.5
## - HeatingQC 4 0.1509 15.758 -6274.4
## - LandSlope 2 0.1174 15.724 -6273.5
## - LandContour 3 0.1392 15.746 -6273.5
## - GarageArea 1 0.0995 15.706 -6273.2
## + RoofStyle 5 0.0252 15.581 -6272.7
## - Exterior1st 14 0.4057 16.012 -6271.1
## - GarageCars 1 0.1227 15.729 -6271.0
## - Heating 5 0.2121 15.819 -6270.8
## - CentralAir 1 0.1395 15.746 -6269.5
## - LotConfig 4 0.2065 15.813 -6269.3
## - Foundation 5 0.2428 15.849 -6268.0
## - BsmtFullBath 1 0.1558 15.762 -6268.0
## - SaleType 8 0.3186 15.925 -6267.1
## - BsmtUnfSF 1 0.1662 15.773 -6267.0
## - BsmtFinSF2 1 0.1690 15.776 -6266.8
## - WoodDeckSF 1 0.1795 15.786 -6265.8
## - KitchenQual 3 0.2291 15.836 -6265.2
## + Exterior2nd 14 0.1319 15.475 -6264.7
## - Fireplaces 1 0.2236 15.830 -6261.7
## - LotArea 1 0.2339 15.841 -6260.8
## - ScreenPorch 1 0.3087 15.915 -6254.0
## - SaleCondition 5 0.4271 16.034 -6251.2
## - YearBuilt 1 0.4116 16.018 -6244.6
## - Condition1 8 0.6230 16.230 -6239.6
## - BsmtFinSF1 1 0.5813 16.188 -6229.3
## - Functional 6 0.7493 16.356 -6224.3
## - X2ndFlrSF 1 0.8588 16.465 -6204.7
## - MSZoning 4 1.0194 16.626 -6196.6
## - OverallCond 1 1.1102 16.717 -6182.7
## - OverallQual 1 1.2360 16.843 -6171.8
## - X1stFlrSF 1 1.2883 16.895 -6167.3
## - Neighborhood 24 1.9720 17.579 -6155.7
## - RoofMatl 7 3.6770 19.284 -5987.4
##
## Step: AIC=-6281.09
## logSalePrice ~ MSSubClass + MSZoning + LotArea + Street + LandContour +
## Utilities + LotConfig + LandSlope + Neighborhood + Condition1 +
## BldgType + HouseStyle + OverallQual + OverallCond + YearBuilt +
## YearRemodAdd + RoofMatl + Exterior1st + ExterCond + Foundation +
## BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC +
## CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath +
## FullBath + HalfBath + KitchenAbvGr + KitchenQual + TotRmsAbvGrd +
## Functional + Fireplaces + GarageCars + GarageArea + WoodDeckSF +
## OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch +
## PoolArea + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - OpenPorchSF 1 0.0185 15.639 -6281.4
## - HouseStyle 7 0.1491 15.770 -6281.3
## <none> 15.620 -6281.1
## + Id 1 0.0139 15.607 -6280.4
## - PoolArea 1 0.0332 15.654 -6280.0
## + MoSold 1 0.0087 15.612 -6279.9
## - MSSubClass 1 0.0348 15.655 -6279.9
## + BedroomAbvGr 1 0.0078 15.613 -6279.8
## + BsmtHalfBath 1 0.0036 15.617 -6279.4
## + MiscVal 1 0.0020 15.618 -6279.3
## + MasVnrType 3 0.0449 15.576 -6279.3
## + PavedDrive 2 0.0233 15.597 -6279.3
## + YrSold 1 0.0008 15.620 -6279.2
## - FullBath 1 0.0426 15.663 -6279.1
## + MasVnrArea 1 0.0004 15.620 -6279.1
## + LotShape 3 0.0432 15.577 -6279.1
## - Utilities 1 0.0443 15.665 -6279.0
## - Street 1 0.0453 15.666 -6278.9
## - ExterCond 4 0.1126 15.733 -6278.7
## - X3SsnPorch 1 0.0520 15.673 -6278.3
## - LowQualFinSF 1 0.0563 15.677 -6277.9
## - HalfBath 1 0.0610 15.682 -6277.4
## - KitchenAbvGr 1 0.0614 15.682 -6277.4
## - EnclosedPorch 1 0.0656 15.686 -6277.0
## - TotRmsAbvGrd 1 0.0661 15.687 -6277.0
## - YearRemodAdd 1 0.0742 15.695 -6276.2
## + Electrical 4 0.0333 15.587 -6276.2
## + ExterQual 3 0.0034 15.617 -6275.4
## - HeatingQC 4 0.1498 15.770 -6275.2
## - BldgType 4 0.1510 15.771 -6275.1
## - LandSlope 2 0.1169 15.738 -6274.3
## - LandContour 3 0.1390 15.759 -6274.2
## - GarageArea 1 0.0981 15.719 -6274.0
## + RoofStyle 5 0.0237 15.597 -6273.3
## - Exterior1st 14 0.4055 16.026 -6271.9
## - GarageCars 1 0.1220 15.742 -6271.8
## - Heating 5 0.2175 15.838 -6271.0
## - CentralAir 1 0.1365 15.757 -6270.5
## - LotConfig 4 0.2104 15.831 -6269.7
## - BsmtFullBath 1 0.1544 15.775 -6268.8
## - Foundation 5 0.2416 15.862 -6268.8
## - SaleType 8 0.3144 15.935 -6268.2
## - BsmtUnfSF 1 0.1676 15.788 -6267.6
## - BsmtFinSF2 1 0.1708 15.791 -6267.3
## - KitchenQual 3 0.2253 15.846 -6266.3
## - WoodDeckSF 1 0.1820 15.803 -6266.3
## + Exterior2nd 14 0.1337 15.487 -6265.6
## - Fireplaces 1 0.2263 15.847 -6262.2
## - LotArea 1 0.2403 15.861 -6260.9
## - ScreenPorch 1 0.3093 15.930 -6254.6
## - SaleCondition 5 0.4255 16.046 -6252.1
## - YearBuilt 1 0.4225 16.043 -6244.4
## - Condition1 8 0.6230 16.244 -6240.3
## - BsmtFinSF1 1 0.5862 16.207 -6229.6
## - Functional 6 0.7515 16.372 -6224.9
## - X2ndFlrSF 1 0.8679 16.488 -6204.6
## - MSZoning 4 1.0170 16.637 -6197.6
## - OverallCond 1 1.1109 16.732 -6183.4
## - OverallQual 1 1.2470 16.867 -6171.6
## - X1stFlrSF 1 1.2887 16.909 -6168.1
## - Neighborhood 24 1.9810 17.602 -6155.8
## - RoofMatl 7 3.7029 19.323 -5986.4
##
## Step: AIC=-6281.37
## logSalePrice ~ MSSubClass + MSZoning + LotArea + Street + LandContour +
## Utilities + LotConfig + LandSlope + Neighborhood + Condition1 +
## BldgType + HouseStyle + OverallQual + OverallCond + YearBuilt +
## YearRemodAdd + RoofMatl + Exterior1st + ExterCond + Foundation +
## BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC +
## CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath +
## FullBath + HalfBath + KitchenAbvGr + KitchenQual + TotRmsAbvGrd +
## Functional + Fireplaces + GarageCars + GarageArea + WoodDeckSF +
## EnclosedPorch + X3SsnPorch + ScreenPorch + PoolArea + SaleType +
## SaleCondition
##
## Df Sum of Sq RSS AIC
## - HouseStyle 7 0.1486 15.788 -6281.6
## <none> 15.639 -6281.4
## + OpenPorchSF 1 0.0185 15.620 -6281.1
## + Id 1 0.0135 15.626 -6280.6
## - PoolArea 1 0.0328 15.672 -6280.3
## - MSSubClass 1 0.0346 15.674 -6280.2
## + MoSold 1 0.0070 15.632 -6280.0
## + BedroomAbvGr 1 0.0069 15.632 -6280.0
## + BsmtHalfBath 1 0.0037 15.635 -6279.7
## + MiscVal 1 0.0021 15.637 -6279.6
## + MasVnrType 3 0.0449 15.594 -6279.5
## + YrSold 1 0.0015 15.638 -6279.5
## - Utilities 1 0.0417 15.681 -6279.5
## + PavedDrive 2 0.0223 15.617 -6279.4
## + MasVnrArea 1 0.0002 15.639 -6279.4
## - Street 1 0.0436 15.683 -6279.3
## + LotShape 3 0.0426 15.597 -6279.3
## - FullBath 1 0.0446 15.684 -6279.2
## - X3SsnPorch 1 0.0504 15.689 -6278.7
## - ExterCond 4 0.1159 15.755 -6278.7
## - LowQualFinSF 1 0.0570 15.696 -6278.1
## - EnclosedPorch 1 0.0606 15.700 -6277.8
## - KitchenAbvGr 1 0.0628 15.702 -6277.6
## - TotRmsAbvGrd 1 0.0653 15.704 -6277.3
## - HalfBath 1 0.0683 15.707 -6277.1
## - YearRemodAdd 1 0.0735 15.713 -6276.6
## + Electrical 4 0.0331 15.606 -6276.4
## - HeatingQC 4 0.1486 15.788 -6275.7
## + ExterQual 3 0.0025 15.637 -6275.6
## - BldgType 4 0.1540 15.793 -6275.2
## - LandContour 3 0.1385 15.777 -6274.6
## - LandSlope 2 0.1211 15.760 -6274.2
## - GarageArea 1 0.1008 15.740 -6274.1
## + RoofStyle 5 0.0215 15.618 -6273.4
## - GarageCars 1 0.1173 15.756 -6272.5
## - Exterior1st 14 0.4040 16.043 -6272.4
## - CentralAir 1 0.1311 15.770 -6271.3
## - Heating 5 0.2226 15.862 -6270.9
## - LotConfig 4 0.2111 15.850 -6269.9
## - SaleType 8 0.3075 15.947 -6269.1
## - Foundation 5 0.2492 15.888 -6268.4
## - BsmtFullBath 1 0.1627 15.802 -6268.4
## - BsmtUnfSF 1 0.1726 15.812 -6267.4
## - BsmtFinSF2 1 0.1746 15.814 -6267.3
## - WoodDeckSF 1 0.1757 15.815 -6267.2
## - KitchenQual 3 0.2251 15.864 -6266.6
## + Exterior2nd 14 0.1372 15.502 -6266.2
## - Fireplaces 1 0.2316 15.871 -6262.0
## - LotArea 1 0.2457 15.885 -6260.8
## - ScreenPorch 1 0.3118 15.951 -6254.7
## - SaleCondition 5 0.4237 16.063 -6252.6
## - YearBuilt 1 0.4251 16.064 -6244.5
## - Condition1 8 0.6151 16.254 -6241.4
## - BsmtFinSF1 1 0.5895 16.229 -6229.7
## - Functional 6 0.7479 16.387 -6225.6
## - X2ndFlrSF 1 0.8851 16.524 -6203.5
## - MSZoning 4 1.0080 16.647 -6198.7
## - OverallCond 1 1.1209 16.760 -6182.9
## - OverallQual 1 1.2515 16.891 -6171.7
## - X1stFlrSF 1 1.3144 16.953 -6166.3
## - Neighborhood 24 1.9680 17.607 -6157.4
## - RoofMatl 7 3.6942 19.333 -5987.7
##
## Step: AIC=-6281.65
## logSalePrice ~ MSSubClass + MSZoning + LotArea + Street + LandContour +
## Utilities + LotConfig + LandSlope + Neighborhood + Condition1 +
## BldgType + OverallQual + OverallCond + YearBuilt + YearRemodAdd +
## RoofMatl + Exterior1st + ExterCond + Foundation + BsmtFinSF1 +
## BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC + CentralAir +
## X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + FullBath +
## HalfBath + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional +
## Fireplaces + GarageCars + GarageArea + WoodDeckSF + EnclosedPorch +
## X3SsnPorch + ScreenPorch + PoolArea + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## - MSSubClass 1 0.0004 15.788 -6283.6
## <none> 15.788 -6281.6
## - Utilities 1 0.0243 15.812 -6281.4
## + HouseStyle 7 0.1486 15.639 -6281.4
## + OpenPorchSF 1 0.0181 15.770 -6281.3
## + MoSold 1 0.0100 15.778 -6280.6
## + Id 1 0.0098 15.778 -6280.5
## - PoolArea 1 0.0338 15.822 -6280.5
## + BsmtHalfBath 1 0.0071 15.781 -6280.3
## + BedroomAbvGr 1 0.0033 15.784 -6279.9
## + MiscVal 1 0.0020 15.786 -6279.8
## + MasVnrType 3 0.0451 15.743 -6279.8
## - FullBath 1 0.0420 15.830 -6279.8
## + YrSold 1 0.0014 15.786 -6279.8
## + PavedDrive 2 0.0230 15.765 -6279.8
## + MasVnrArea 1 0.0001 15.788 -6279.7
## - Street 1 0.0456 15.833 -6279.5
## + LotShape 3 0.0377 15.750 -6279.1
## - X3SsnPorch 1 0.0539 15.842 -6278.7
## - KitchenAbvGr 1 0.0584 15.846 -6278.3
## - ExterCond 4 0.1260 15.914 -6278.1
## - HalfBath 1 0.0654 15.853 -6277.6
## - LowQualFinSF 1 0.0674 15.855 -6277.5
## - TotRmsAbvGrd 1 0.0700 15.858 -6277.2
## - YearRemodAdd 1 0.0733 15.861 -6276.9
## - EnclosedPorch 1 0.0739 15.862 -6276.9
## + Electrical 4 0.0348 15.753 -6276.8
## - LandContour 3 0.1190 15.907 -6276.8
## - HeatingQC 4 0.1459 15.934 -6276.3
## + ExterQual 3 0.0061 15.782 -6276.2
## - LandSlope 2 0.1159 15.904 -6275.0
## - GarageArea 1 0.0980 15.886 -6274.7
## + RoofStyle 5 0.0239 15.764 -6273.8
## - Exterior1st 14 0.3996 16.187 -6273.4
## - BldgType 4 0.1819 15.970 -6273.0
## - GarageCars 1 0.1176 15.905 -6272.9
## - CentralAir 1 0.1342 15.922 -6271.4
## - LotConfig 4 0.2091 15.997 -6270.5
## - Heating 5 0.2342 16.022 -6270.3
## - Foundation 5 0.2343 16.022 -6270.3
## - SaleType 8 0.3072 16.095 -6269.7
## - BsmtFullBath 1 0.1577 15.945 -6269.2
## - BsmtUnfSF 1 0.1721 15.960 -6267.9
## - KitchenQual 3 0.2171 16.005 -6267.8
## - WoodDeckSF 1 0.1741 15.962 -6267.7
## - BsmtFinSF2 1 0.1802 15.968 -6267.2
## + Exterior2nd 14 0.1396 15.648 -6266.5
## - Fireplaces 1 0.2486 16.036 -6261.0
## - LotArea 1 0.2595 16.047 -6260.0
## - ScreenPorch 1 0.3093 16.097 -6255.5
## - SaleCondition 5 0.4629 16.251 -6249.7
## - Condition1 8 0.6048 16.392 -6243.1
## - YearBuilt 1 0.4627 16.250 -6241.7
## - BsmtFinSF1 1 0.6059 16.394 -6229.0
## - Functional 6 0.7576 16.545 -6225.6
## - MSZoning 4 0.9526 16.740 -6204.6
## - OverallCond 1 1.1181 16.906 -6184.4
## - X1stFlrSF 1 1.3735 17.161 -6162.6
## - Neighborhood 24 1.9489 17.737 -6160.7
## - OverallQual 1 1.3979 17.186 -6160.5
## - X2ndFlrSF 1 1.5027 17.290 -6151.7
## - RoofMatl 7 3.7558 19.544 -5986.0
##
## Step: AIC=-6283.61
## logSalePrice ~ MSZoning + LotArea + Street + LandContour + Utilities +
## LotConfig + LandSlope + Neighborhood + Condition1 + BldgType +
## OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofMatl +
## Exterior1st + ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 +
## BsmtUnfSF + Heating + HeatingQC + CentralAir + X1stFlrSF +
## X2ndFlrSF + LowQualFinSF + BsmtFullBath + FullBath + HalfBath +
## KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional +
## Fireplaces + GarageCars + GarageArea + WoodDeckSF + EnclosedPorch +
## X3SsnPorch + ScreenPorch + PoolArea + SaleType + SaleCondition
##
## Df Sum of Sq RSS AIC
## <none> 15.788 -6283.6
## - Utilities 1 0.0246 15.813 -6283.4
## + OpenPorchSF 1 0.0180 15.770 -6283.3
## + MoSold 1 0.0098 15.778 -6282.5
## + Id 1 0.0097 15.778 -6282.5
## - PoolArea 1 0.0339 15.822 -6282.5
## + BsmtHalfBath 1 0.0073 15.781 -6282.3
## + BedroomAbvGr 1 0.0033 15.785 -6281.9
## + MiscVal 1 0.0020 15.786 -6281.8
## + MasVnrType 3 0.0453 15.743 -6281.8
## - FullBath 1 0.0420 15.830 -6281.8
## + YrSold 1 0.0014 15.787 -6281.7
## + PavedDrive 2 0.0231 15.765 -6281.7
## + MSSubClass 1 0.0004 15.788 -6281.6
## + MasVnrArea 1 0.0001 15.788 -6281.6
## - Street 1 0.0455 15.834 -6281.4
## + LotShape 3 0.0372 15.751 -6281.0
## - X3SsnPorch 1 0.0536 15.842 -6280.7
## - KitchenAbvGr 1 0.0585 15.847 -6280.2
## + HouseStyle 7 0.1145 15.674 -6280.2
## - ExterCond 4 0.1258 15.914 -6280.1
## - HalfBath 1 0.0654 15.854 -6279.6
## - LowQualFinSF 1 0.0682 15.856 -6279.4
## - TotRmsAbvGrd 1 0.0704 15.859 -6279.1
## - YearRemodAdd 1 0.0730 15.861 -6278.9
## + Electrical 4 0.0346 15.754 -6278.8
## - EnclosedPorch 1 0.0747 15.863 -6278.8
## - LandContour 3 0.1192 15.907 -6278.7
## - HeatingQC 4 0.1455 15.934 -6278.3
## + ExterQual 3 0.0057 15.783 -6278.1
## - LandSlope 2 0.1160 15.904 -6277.0
## - GarageArea 1 0.0982 15.886 -6276.6
## + RoofStyle 5 0.0230 15.765 -6275.7
## - Exterior1st 14 0.3994 16.188 -6275.4
## - GarageCars 1 0.1177 15.906 -6274.8
## - CentralAir 1 0.1342 15.922 -6273.3
## - LotConfig 4 0.2101 15.998 -6272.4
## - Heating 5 0.2353 16.023 -6272.1
## - Foundation 5 0.2356 16.024 -6272.1
## - SaleType 8 0.3082 16.096 -6271.6
## - BsmtFullBath 1 0.1602 15.948 -6271.0
## - KitchenQual 3 0.2170 16.005 -6269.8
## - WoodDeckSF 1 0.1738 15.962 -6269.7
## - BsmtUnfSF 1 0.1745 15.963 -6269.7
## - BsmtFinSF2 1 0.1806 15.969 -6269.1
## - BldgType 4 0.2511 16.039 -6268.7
## + Exterior2nd 14 0.1397 15.649 -6268.5
## - Fireplaces 1 0.2501 16.038 -6262.8
## - LotArea 1 0.2592 16.047 -6262.0
## - ScreenPorch 1 0.3090 16.097 -6257.5
## - SaleCondition 5 0.4629 16.251 -6251.7
## - Condition1 8 0.6056 16.394 -6245.0
## - YearBuilt 1 0.4625 16.251 -6243.7
## - BsmtFinSF1 1 0.6167 16.405 -6230.0
## - Functional 6 0.7579 16.546 -6227.6
## - MSZoning 4 0.9533 16.741 -6206.5
## - OverallCond 1 1.1220 16.910 -6186.0
## - X1stFlrSF 1 1.3731 17.161 -6164.6
## - Neighborhood 24 1.9491 17.737 -6162.7
## - OverallQual 1 1.4200 17.208 -6160.6
## - X2ndFlrSF 1 1.6497 17.438 -6141.4
## - RoofMatl 7 3.7956 19.584 -5985.0lm.house.aic$anova## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## logSalePrice ~ (Id + MSSubClass + MSZoning + LotArea + Street +
## LotShape + LandContour + Utilities + LotConfig + LandSlope +
## Neighborhood + Condition1 + BldgType + HouseStyle + OverallQual +
## OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl +
## Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + ExterQual +
## ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF +
## TotalBsmtSF + Heating + HeatingQC + CentralAir + Electrical +
## X1stFlrSF + X2ndFlrSF + LowQualFinSF + GrLivArea + BsmtFullBath +
## BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr +
## KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageCars +
## GarageArea + PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch +
## X3SsnPorch + ScreenPorch + PoolArea + MiscVal + MoSold +
## YrSold + SaleType + SaleCondition + SalePrice) - SalePrice
##
## Final Model:
## logSalePrice ~ MSZoning + LotArea + Street + LandContour + Utilities +
## LotConfig + LandSlope + Neighborhood + Condition1 + BldgType +
## OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofMatl +
## Exterior1st + ExterCond + Foundation + BsmtFinSF1 + BsmtFinSF2 +
## BsmtUnfSF + Heating + HeatingQC + CentralAir + X1stFlrSF +
## X2ndFlrSF + LowQualFinSF + BsmtFullBath + FullBath + HalfBath +
## KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional +
## Fireplaces + GarageCars + GarageArea + WoodDeckSF + EnclosedPorch +
## X3SsnPorch + ScreenPorch + PoolArea + SaleType + SaleCondition
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 1263 15.24812 -6234.106
## 2 - GrLivArea 0 0.0000000000 1263 15.24812 -6234.106
## 3 - TotalBsmtSF 0 0.0000000000 1263 15.24812 -6234.106
## 4 - Exterior2nd 14 0.1315808781 1277 15.37970 -6249.639
## 5 - RoofStyle 5 0.0426657803 1282 15.42237 -6255.619
## 6 - ExterQual 3 0.0063114188 1285 15.42868 -6261.025
## 7 - Electrical 4 0.0380993793 1289 15.46678 -6265.447
## 8 - PavedDrive 2 0.0210810403 1291 15.48786 -6267.470
## 9 - MiscVal 1 0.0005240783 1292 15.48838 -6269.421
## 10 - MasVnrArea 1 0.0018410751 1293 15.49022 -6271.249
## 11 - BsmtHalfBath 1 0.0020223081 1294 15.49225 -6273.059
## 12 - YrSold 1 0.0028774765 1295 15.49512 -6274.790
## 13 - LotShape 3 0.0484550518 1298 15.54358 -6276.259
## 14 - MasVnrType 3 0.0458185046 1301 15.58940 -6277.988
## 15 - MoSold 1 0.0090278220 1302 15.59842 -6279.148
## 16 - BedroomAbvGr 1 0.0082389555 1303 15.60666 -6280.382
## 17 - Id 1 0.0138832408 1304 15.62055 -6281.092
## 18 - OpenPorchSF 1 0.0185382931 1305 15.63908 -6281.371
## 19 - HouseStyle 7 0.1486418019 1312 15.78773 -6281.645
## 20 - MSSubClass 1 0.0004194046 1313 15.78815 -6283.607SVD Regression
house.svd = house
house.svd$SalePrice = NULL
cols = names(house.int)
cols = cols[cols!="SalePrice"]
cols = c(cols, "logSalePrice")
house.scale = house.svd
house.scale[,cols] = lapply(house.svd[,cols], function(x) { scale(x, center = TRUE, scale = TRUE)})
house.modmat = model.matrix(logSalePrice~., data = house.scale)
plot.svd.reg <- function(df, k){
p1 <- ggplot(df) +
geom_point(aes(score, resids), size = 2) +
stat_smooth(aes(score, resids)) +
ggtitle('Residuals vs. fitted values')
p2 <- ggplot(df, aes(resids)) +
geom_histogram(aes(y = ..density..)) +
geom_density(color = 'red', fill = 'red', alpha = 0.2) +
ggtitle('Histogram of residuals')
qqnorm(df$resids)
grid.arrange(p1, p2, ncol = 2)
df$std.resids = sqrt((df$resids - mean(df$resids))^2)
p3 = ggplot(df) +
geom_point(aes(score, std.resids), size = 2) +
stat_smooth(aes(score, std.resids)) +
ggtitle('Standardized residuals vs. fitted values')
print(p3)
n = nrow(df)
Ybar = mean(df$logSalePrice)
SST <- sum((df$logSalePrice - Ybar)^2)
SSR <- sum(df$resids * df$resids)
SSE = SST - SSR
RMSE = sqrt(SSR/(n-2))
cat(paste('SSE =', as.character(SSE), '\n'))
cat(paste('SSR =', as.character(SSR), '\n'))
cat(paste('SST =', as.character(SSE + SSR), '\n'))
cat(paste('RMSE =', as.character(SSE/(n - 2)), '\n'))
adjR2 <- 1.0 - (SSR/SST) * ((n - 1)/(n - k - 1))
cat(paste('Adjusted R^2 =', as.character(adjR2)), '\n')
}
M = house.modmat[,-1]
M2 = t(M)%*%M
# head(M2)
mSVD = svd(M2)
plot(log(mSVD$d))
inv.diag = rep(0, length(mSVD$d))
inv.diag[1:190] = 1/mSVD$d[1:190]
mD = diag(inv.diag)
#Inverse (t(M)*M) = V Diag U
mInV = mSVD$v %*% mD %*% t(mSVD$u)
b = house.scale$logSalePrice
#x = Inv(MTM)*t(M)*b
x = mInV %*% t(M) %*% b
x = ginv(M) %*% b
house.cp = house
house.cp$score = (M %*% x)*sd(house.cp$logSalePrice) + mean(house.cp$logSalePrice)
house.cp$resids = house.cp$score - house.cp$logSalePrice
RSS = sum((house.cp$logSalePrice - (house.cp$score))^2)
RSS## [1] 16.41259TSS = sum((house.cp$logSalePrice - mean(house.cp$logSalePrice))^2)
TSS## [1] 231.4222require(repr)
options(repr.pmales.extlot.width=8, repr.plot.height=4)
plot## function (x, y, ...)
## UseMethod("plot")
## <bytecode: 0x1038198>
## <environment: namespace:graphics>Elastic Net Regression
